Optimal image representations for mass detection in digital mammography

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(1)Optimal Image Representations For Mass Detection In Digital Mammography Matteo Masotti University of Bologna – Department of Physics Medical Imaging Group. June 1, 2005. Matteo Masotti. June 1, 2005 – PhD Defense.

(2) Outline. 1. Digital Mammography. Matteo Masotti. June 1, 2005 – PhD Defense.

(3) Outline. 1. Digital Mammography. 2. Two–Class Pattern Classification. Matteo Masotti. June 1, 2005 – PhD Defense.

(4) Outline. 1. Digital Mammography. 2. Two–Class Pattern Classification. 3. Exploring Image Representations. Matteo Masotti. June 1, 2005 – PhD Defense.

(5) Outline. 1. Digital Mammography. 2. Two–Class Pattern Classification. 3. Exploring Image Representations. 4. CAD System Implementation. Matteo Masotti. June 1, 2005 – PhD Defense.

(6) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Outline. 1. Digital Mammography. 2. Two–Class Pattern Classification. 3. Exploring Image Representations. 4. CAD System Implementation. Matteo Masotti. June 1, 2005 – PhD Defense.

(7) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Breast Cancer – Definition An uncontrolled and rapid proliferation of cells in a specific part of the body may lead to either:. Matteo Masotti. June 1, 2005 – PhD Defense.

(8) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Breast Cancer – Definition An uncontrolled and rapid proliferation of cells in a specific part of the body may lead to either: benign tumor 7→ local and circumscribed abnormal growth of tissue. Matteo Masotti. June 1, 2005 – PhD Defense.

(9) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Breast Cancer – Definition An uncontrolled and rapid proliferation of cells in a specific part of the body may lead to either: benign tumor 7→ local and circumscribed abnormal growth of tissue malignant tumor (cancer) 7→ abnormal growth of tissue comprised of cells that may invade neighboring organs and replace normal tissue (metastasis). Matteo Masotti. June 1, 2005 – PhD Defense.

(10) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Breast Cancer – Definition An uncontrolled and rapid proliferation of cells in a specific part of the body may lead to either: benign tumor 7→ local and circumscribed abnormal growth of tissue malignant tumor (cancer) 7→ abnormal growth of tissue comprised of cells that may invade neighboring organs and replace normal tissue (metastasis) Breast cancer 7→ malignant tumor developed from cells of the breast. Matteo Masotti. June 1, 2005 – PhD Defense.

(11) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Breast Cancer – Signs The most common signs of breast cancer are:. Matteo Masotti. June 1, 2005 – PhD Defense.

(12) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Breast Cancer – Signs The most common signs of breast cancer are: Masses. thickenings of the breast tissue with size 3–30 (mm). Matteo Masotti. June 1, 2005 – PhD Defense.

(13) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Breast Cancer – Signs The most common signs of breast cancer are: Masses. Micro–calcifications. thickenings of the breast tissue with size 3–30 (mm). small spots in the breast tissue with size 0.1–0.3 (mm). Matteo Masotti. June 1, 2005 – PhD Defense.

(14) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Breast Cancer – Incidence And Mortality Incidence: World Health Organization 7→ 1.3 million people will be diagnosed with breast cancer in 2005 worldwide. Matteo Masotti. June 1, 2005 – PhD Defense.

(15) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Breast Cancer – Incidence And Mortality Incidence: World Health Organization 7→ 1.3 million people will be diagnosed with breast cancer in 2005 worldwide Mortality: American Cancer Society 7→ 41000 people will die from breast cancer in the United States during 2005. Matteo Masotti. June 1, 2005 – PhD Defense.

(16) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Breast Cancer – Incidence And Mortality Incidence: World Health Organization 7→ 1.3 million people will be diagnosed with breast cancer in 2005 worldwide Mortality: American Cancer Society 7→ 41000 people will die from breast cancer in the United States during 2005 ⇒ Screening mammography: earlier detection through periodical X-ray breast examination performed on asymptomatic patients is fundamental Matteo Masotti. June 1, 2005 – PhD Defense.

(17) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Screening Mammography – Breast Examination The left and right breasts of the patient are both exposed to X–rays. . .. Matteo Masotti. June 1, 2005 – PhD Defense.

(18) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Screening Mammography – Breast Examination The left and right breasts of the patient are both exposed to X–rays. . .. Matteo Masotti. . . . and mammographic digital images are obtained for each breast at different views. June 1, 2005 – PhD Defense.

(19) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Screening Mammography – Radiologists’ Detection The radiologist looks carefully at each mammographic digital image. . .. Matteo Masotti. June 1, 2005 – PhD Defense.

(20) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Screening Mammography – Radiologists’ Detection The radiologist looks carefully at each mammographic digital image. . .. Matteo Masotti. . . . and marks the regions suspected to be potential breast tumors. June 1, 2005 – PhD Defense.

(21) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Screening Mammography – Radiologists’ Performances. It has been demonstrated that radiologists may miss 15–30% of breast lesions. Matteo Masotti. June 1, 2005 – PhD Defense.

(22) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Screening Mammography – Radiologists’ Performances. It has been demonstrated that radiologists may miss 15–30% of breast lesions Missed detections may be due to: subtle nature of the radiographic findings poor image quality eye fatigue. Matteo Masotti. June 1, 2005 – PhD Defense.

(23) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Screening Mammography – Radiologists’ Performances. It has been demonstrated that radiologists may miss 15–30% of breast lesions Missed detections may be due to: subtle nature of the radiographic findings poor image quality eye fatigue ⇒ Computer–Aided Detection (CAD) systems are commonly used as second readers to increase the efficiency of screening procedures. Matteo Masotti. June 1, 2005 – PhD Defense.

(24) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Screening Mammography – Computer–Aided Detection In order to automatically implement mass detection, first each mammographic digital image must be scanned. . .. Matteo Masotti. June 1, 2005 – PhD Defense.

(25) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Screening Mammography – Computer–Aided Detection In order to automatically implement mass detection, first each mammographic digital image must be scanned. . .. Matteo Masotti. . . . then for each scanned region (a.k.a. crop). June 1, 2005 – PhD Defense.

(26) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Breast Cancer Screening Mammography. Screening Mammography – Computer–Aided Detection In order to automatically implement mass detection, first each mammographic digital image must be scanned. . .. . . . then for each scanned region (a.k.a. crop). What is that? A mass or a non–mass?. Matteo Masotti. June 1, 2005 – PhD Defense.

(27) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Outline. 1. Digital Mammography. 2. Two–Class Pattern Classification. 3. Exploring Image Representations. 4. CAD System Implementation. Matteo Masotti. June 1, 2005 – PhD Defense.

(28) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Problem Set Up – Flow Diagram. The Two Classes. Matteo Masotti. June 1, 2005 – PhD Defense.

(29) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Problem Set Up – Flow Diagram. The Two Classes. 7→. Matteo Masotti. June 1, 2005 – PhD Defense.

(30) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Problem Set Up – Flow Diagram. The Two Classes. 7→. Features. Matteo Masotti. June 1, 2005 – PhD Defense.

(31) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Problem Set Up – Flow Diagram. The Two Classes. 7→. Features. Matteo Masotti. 7→. June 1, 2005 – PhD Defense.

(32) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Problem Set Up – Flow Diagram. The Two Classes. 7→. Features. Matteo Masotti. 7→. June 1, 2005 – PhD Defense. Classifier.

(33) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. The Two Classes – Flow Diagram. The Two Classes. 7→. Features. Matteo Masotti. 7→. June 1, 2005 – PhD Defense. Classifier.

(34) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. The Two Classes – Masses Vs. Non–Masses What is that? A mass or a non–mass?. Matteo Masotti. June 1, 2005 – PhD Defense.

(35) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. The Two Classes – Masses Vs. Non–Masses What is that? A mass or a non–mass? This actually means separating two classes. . .. Matteo Masotti. June 1, 2005 – PhD Defense.

(36) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. The Two Classes – Masses Vs. Non–Masses What is that? A mass or a non–mass? This actually means separating two classes. . . Mass class. Matteo Masotti. June 1, 2005 – PhD Defense.

(37) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. The Two Classes – Masses Vs. Non–Masses What is that? A mass or a non–mass? This actually means separating two classes. . . Non–mass class. Mass class. Matteo Masotti. June 1, 2005 – PhD Defense.

(38) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Features – Flow Diagram. The Two Classes Masses. 7→. Features. 7→. Non–masses. Matteo Masotti. June 1, 2005 – PhD Defense. Classifier.

(39) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Features – Pixels, Wavelets, Ranklets Features should be chosen as to emphasize discriminant characteristics of the two classes. Matteo Masotti. June 1, 2005 – PhD Defense.

(40) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Features – Pixels, Wavelets, Ranklets Features should be chosen as to emphasize discriminant characteristics of the two classes Explored features:. Matteo Masotti. June 1, 2005 – PhD Defense.

(41) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Features – Pixels, Wavelets, Ranklets Features should be chosen as to emphasize discriminant characteristics of the two classes Explored features: Pixels. Matteo Masotti. June 1, 2005 – PhD Defense.

(42) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Features – Pixels, Wavelets, Ranklets Features should be chosen as to emphasize discriminant characteristics of the two classes Explored features: Pixels Wavelets. Matteo Masotti. June 1, 2005 – PhD Defense.

(43) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Features – Pixels, Wavelets, Ranklets Features should be chosen as to emphasize discriminant characteristics of the two classes Explored features: Pixels Wavelets Ranklets. Matteo Masotti. June 1, 2005 – PhD Defense.

(44) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Features – Pixels, Wavelets, Ranklets Features should be chosen as to emphasize discriminant characteristics of the two classes Explored features: Pixels Wavelets Ranklets Notice, in this problem features ≡ image representations. Matteo Masotti. June 1, 2005 – PhD Defense.

(45) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Features – Pixels, Wavelets, Ranklets Features should be chosen as to emphasize discriminant characteristics of the two classes Explored features: Pixels Wavelets Ranklets Notice, in this problem features ≡ image representations (Much more details in the next section. . . ). Matteo Masotti. June 1, 2005 – PhD Defense.

(46) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – Flow Diagram. Features. The Two Classes Masses Non–masses. 7→. Pixels. 7→. Wavelets Ranklets. Matteo Masotti. June 1, 2005 – PhD Defense. Classifier.

(47) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – Notation Suppose that some samples {xi , yi }, i = 1, . . . , l taken from some data distribution are given:. Matteo Masotti. June 1, 2005 – PhD Defense.

(48) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – Notation Suppose that some samples {xi , yi }, i = 1, . . . , l taken from some data distribution are given: yi ∈ {−1, +1} are the labels representing the class membership of each sample. Matteo Masotti. June 1, 2005 – PhD Defense.

(49) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – Notation Suppose that some samples {xi , yi }, i = 1, . . . , l taken from some data distribution are given: yi ∈ {−1, +1} are the labels representing the class membership of each sample xi ∈ Rd are the features characterizing each sample. Matteo Masotti. June 1, 2005 – PhD Defense.

(50) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – Notation Suppose that some samples {xi , yi }, i = 1, . . . , l taken from some data distribution are given: yi ∈ {−1, +1} are the labels representing the class membership of each sample xi ∈ Rd are the features characterizing each sample In this problem:. Matteo Masotti. June 1, 2005 – PhD Defense.

(51) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – Notation Suppose that some samples {xi , yi }, i = 1, . . . , l taken from some data distribution are given: yi ∈ {−1, +1} are the labels representing the class membership of each sample xi ∈ Rd are the features characterizing each sample In this problem: Class Mass Non–mass Matteo Masotti. June 1, 2005 – PhD Defense.

(52) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – Notation Suppose that some samples {xi , yi }, i = 1, . . . , l taken from some data distribution are given: yi ∈ {−1, +1} are the labels representing the class membership of each sample xi ∈ Rd are the features characterizing each sample In this problem: Class. Label. Mass. +1. Non–mass. −1 Matteo Masotti. June 1, 2005 – PhD Defense.

(53) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – Notation Suppose that some samples {xi , yi }, i = 1, . . . , l taken from some data distribution are given: yi ∈ {−1, +1} are the labels representing the class membership of each sample xi ∈ Rd are the features characterizing each sample In this problem: Class. Label. Mass. +1. Non–mass. −1 Matteo Masotti. June 1, 2005 – PhD Defense. Features.

(54) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – Support Vector Machine SVM is a classifier which finds the hyperplane w · x + b = 0 maximizing the margin between the two classes in the training set Train Hyperplane wx + b = 0 Class 2. Support Vectors Class 1 Margin. Matteo Masotti. June 1, 2005 – PhD Defense.

(55) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – Support Vector Machine SVM is a classifier which finds the hyperplane w · x + b = 0 maximizing the margin between the two classes in the training set Test. Train Hyperplane wx + b = 0. Hyperplane wx + b = 0. Class 2. Class 2. Support Vectors Class 1. Class 1. Margin. Margin. Matteo Masotti. June 1, 2005 – PhD Defense.

(56) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – SVM’s Kernels Once SVM has been trained, each new sample x is classified according to: ! l X f (x) = sign αi yi K (x, xi ) + b i=1. Matteo Masotti. June 1, 2005 – PhD Defense.

(57) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – SVM’s Kernels Once SVM has been trained, each new sample x is classified according to: ! l X f (x) = sign αi yi K (x, xi ) + b i=1. Polynomial kernel of degree d: K (x, y) = (γx · y + r )d. Matteo Masotti. June 1, 2005 – PhD Defense.

(58) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – SVM’s Kernels Once SVM has been trained, each new sample x is classified according to: ! l X f (x) = sign αi yi K (x, xi ) + b i=1. Polynomial kernel of degree d: K (x, y) = (γx · y + r )d Radial basis kernel: K (x, y) = exp −γ kx − yk2. Matteo Masotti. June 1, 2005 – PhD Defense.

(59) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – Performances After SVM has been tested on the samples of the test set. . . False Negatives Hyperplane wx + b = 0 Non−Masses True Negatives Masses. True Positives False Positives. Margin. Matteo Masotti. June 1, 2005 – PhD Defense.

(60) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Problem Set Up The Two Classes Features Classifier. Classifier – Performances After SVM has been tested on the samples of the test set. . .. . . . then classification performances are given by using ROC curves. False Negatives. 1. Hyperplane wx + b = 0. True Negatives Masses. True Positives False Positives. Margin. True Positive Fraction. A Non−Masses. An ROC curve 0.5 A better ROC curve. 0. 0. 0.5 False Positive Fraction. Matteo Masotti. June 1, 2005 – PhD Defense. 1.

(61) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Outline. 1. Digital Mammography. 2. Two–Class Pattern Classification. 3. Exploring Image Representations. 4. CAD System Implementation. Matteo Masotti. June 1, 2005 – PhD Defense.

(62) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Flow Diagram. Features. The Two Classes Masses Non–masses. 7→. Pixels. 7→. Wavelets Ranklets. Matteo Masotti. June 1, 2005 – PhD Defense. Classifier SVM.

(63) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Mass Variability. Tumoral masses vary considerably in:. Matteo Masotti. June 1, 2005 – PhD Defense.

(64) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Mass Variability. Tumoral masses vary considerably in: optical density. Matteo Masotti. June 1, 2005 – PhD Defense.

(65) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Mass Variability. Tumoral masses vary considerably in: optical density shape. Matteo Masotti. June 1, 2005 – PhD Defense.

(66) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Mass Variability. Tumoral masses vary considerably in: optical density shape size. Matteo Masotti. June 1, 2005 – PhD Defense.

(67) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Mass Variability. Tumoral masses vary considerably in: optical density shape size border. Matteo Masotti. June 1, 2005 – PhD Defense.

(68) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Mass Variability. Tumoral masses vary considerably in: optical density shape size border. Matteo Masotti. June 1, 2005 – PhD Defense.

(69) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Mass Variability. Tumoral masses vary considerably in: optical density shape size border ⇒ Objective difficulty of characterizing all types of masses with the same few measurable quantities (features). Matteo Masotti. June 1, 2005 – PhD Defense.

(70) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Featureless Approach. Many of the algorithms so far developed:. Matteo Masotti. June 1, 2005 – PhD Defense.

(71) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Featureless Approach. Many of the algorithms so far developed: restrict to a specific type of masses. Matteo Masotti. June 1, 2005 – PhD Defense.

(72) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Featureless Approach. Many of the algorithms so far developed: restrict to a specific type of masses. Matteo Masotti. June 1, 2005 – PhD Defense.

(73) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Featureless Approach. Many of the algorithms so far developed: restrict to a specific type of masses describe the specific type of masses with a specific set of few features. Matteo Masotti. June 1, 2005 – PhD Defense.

(74) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Featureless Approach. Many of the algorithms so far developed: restrict to a specific type of masses describe the specific type of masses with a specific set of few features. Adopted approach:. Matteo Masotti. June 1, 2005 – PhD Defense.

(75) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Featureless Approach. Many of the algorithms so far developed: restrict to a specific type of masses describe the specific type of masses with a specific set of few features. Adopted approach: in order to deal with almost every type of masses, raw/enhanced crops are classified without extracting any a priori feature 7→ featureless approach Matteo Masotti. June 1, 2005 – PhD Defense.

(76) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Material And Methods USF Digital Database for Screening Mammography (DDSM):. Matteo Masotti. June 1, 2005 – PhD Defense.

(77) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Material And Methods USF Digital Database for Screening Mammography (DDSM): 1000 crops representing masses. Matteo Masotti. June 1, 2005 – PhD Defense.

(78) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Material And Methods USF Digital Database for Screening Mammography (DDSM): 1000 crops representing masses 5000 crops representing non–masses. Matteo Masotti. June 1, 2005 – PhD Defense.

(79) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Material And Methods USF Digital Database for Screening Mammography (DDSM): 1000 crops representing masses 5000 crops representing non–masses. Performance evaluation:. Matteo Masotti. June 1, 2005 – PhD Defense.

(80) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Material And Methods USF Digital Database for Screening Mammography (DDSM): 1000 crops representing masses 5000 crops representing non–masses. Performance evaluation: 10–fold cross–validation. Matteo Masotti. June 1, 2005 – PhD Defense.

(81) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Overview – Material And Methods USF Digital Database for Screening Mammography (DDSM): 1000 crops representing masses 5000 crops representing non–masses. Test set. Performance evaluation: 10–fold cross–validation. Fold 1. Entire data set. Matteo Masotti. June 1, 2005 – PhD Defense.

(82) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Pixels – Flow Diagram. Features. The Two Classes Masses Non–masses. 7→. Pixels. 7→. Wavelets Ranklets. Matteo Masotti. June 1, 2005 – PhD Defense. Classifier SVM.

(83) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Pixels – Motivation. Why pixel–based image representations?. Matteo Masotti. June 1, 2005 – PhD Defense.

(84) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Pixels – Motivation. Why pixel–based image representations? To investigate whether the gray–level values of the crops gives enough informations in order to discriminate between masses and non–masses. Matteo Masotti. June 1, 2005 – PhD Defense.

(85) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Pixels – Definition. . . . and its gray–level values   0 0 . . . 201  0 0 . . . 203     0 0 . . . 201     .. .. .. ..   . . . .     147 171 . . . 237     152 205 . . . 237  152 225 . . . 232. A crop. . .. Matteo Masotti. June 1, 2005 – PhD Defense.

(86) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Pixels – Example. Original crop. Equalized crop. Matteo Masotti. Resized crop. June 1, 2005 – PhD Defense.

(87) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Pixels – ROC Curve (Linear Kernel) 1 0.9 0.8. True Positive Fraction. 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0. PixHRS with lin. ker. (256 feat.) PixRS with lin. ker. (256 feat.). 0. 0.02. 0.04. 0.06. 0.08 0.1 0.12 False Positive Fraction. Matteo Masotti. 0.14. 0.16. June 1, 2005 – PhD Defense. 0.18.

(88) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Pixels – Some Numerical Results. PixHRS PixRS. FPF ∼ .01 .70 ± .06 .49 ± .04. FPF ∼ .03 .84 ± .05 .72 ± .05. FPF ∼ .05 .89 ± .03 .82 ± .04. Table: Classification results comparison. The TPF values obtained by the best performing pixel–based image representations are shown, in particular for FPF values approximately equal to .01, .03 and .05. Matteo Masotti. June 1, 2005 – PhD Defense.

(89) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Wavelets – Flow Diagram. Features. The Two Classes Masses Non–masses. 7→. Pixels. 7→. Wavelets Ranklets. Matteo Masotti. June 1, 2005 – PhD Defense. Classifier SVM.

(90) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Wavelets – Motivation. Why wavelet–based image representations?. Matteo Masotti. June 1, 2005 – PhD Defense.

(91) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Wavelets – Motivation. Why wavelet–based image representations? To evaluate whether their ability in enhancing edges and boundaries improve the discrimination between masses and non–masses. Matteo Masotti. June 1, 2005 – PhD Defense.

(92) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Wavelets – Definition 2D discrete wavelet transform (1–level decomposition): Columns. H0 Rows. Rows. H0. 2. Diagonal Detail. L0. 2. Vertical Detail. 2 Columns. Columns. D. V. Rows. Image Columns. L0 Rows. Rows. H0. 2. L0. 2. Horizontal Detail H. 2 Columns. Columns. Matteo Masotti. Rows. June 1, 2005 – PhD Defense. Approximation A.

(93) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Wavelets – Example (Discrete Wavelet Transform) 2D discrete wavelet transform (3–level decomposition): A1. H1. V1. D1. A2. H2. V2. D2. A3. H3. V3. D3. Matteo Masotti. June 1, 2005 – PhD Defense.

(94) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Wavelets – Example (Overcomplete Wavelet Transform) 2D overcomplete wavelet transform (3–level decomposition): H1. V1. D1. H2. V2. D2. H3. V3. D3. Matteo Masotti. June 1, 2005 – PhD Defense.

(95) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Wavelets – ROC Curve (DWT, Linear Kernel) 1 0.9 0.8. True Positive Fraction. 0.7 0.6 0.5 0.4 0.3 0.2 PixHRS with lin. ker. (256 feat.) DwtS with lin. ker. (4096 feat.) DwtHS with lin. ker. (4096 feat.). 0.1 0. 0. 0.02. 0.04. 0.06. 0.08 0.1 0.12 False Positive Fraction. Matteo Masotti. 0.14. 0.16. June 1, 2005 – PhD Defense. 0.18.

(96) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Wavelets – ROC Curve (DWT, Polynomial Kernel) 1 0.9 0.8. True Positive Fraction. 0.7 0.6 0.5 0.4 0.3 0.2 PixHRS with lin. ker. (256 feat.) DwtHS with lin. ker. (4096 feat.) DwtHS2 with pol. ker., degree = 2 (4096 feat.) DwtHS3 with pol. ker., degree = 3 (4096 feat.). 0.1 0. 0. 0.02. 0.04. 0.06. 0.08 0.1 0.12 False Positive Fraction. Matteo Masotti. 0.14. 0.16. June 1, 2005 – PhD Defense. 0.18.

(97) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Wavelets – ROC Curve (OWT, Polynomial Kernel) 1 0.9 0.8. True Positive Fraction. 0.7 0.6 0.5 0.4 0.3 0.2 PixHRS with lin. ker. (256 feat.) DwtHS3 with pol. ker., degree = 3 (4096 feat.) OwtS2 with pol. ker., degree = 2 (~3000 features) OwtHS2 with pol. ker., degree = 2 (~3000 features). 0.1 0. 0. 0.02. 0.04. 0.06. 0.08 0.1 0.12 False Positive Fraction. Matteo Masotti. 0.14. 0.16. June 1, 2005 – PhD Defense. 0.18.

(98) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Wavelets – Some Numerical Results. PixHRS OwtS2 DwtHS3. FPF ∼ .01 .70 ± .06 .62 ± .11. FPF ∼ .03 .84 ± .05 .82 ± .05 .78 ± .04. FPF ∼ .05 .89 ± .03 .87 ± .05 .85 ± .03. Table: Classification results comparison. The TPF values obtained by the best performing pixel–based, DWT–based and OWT–based image representations are shown, in particular for FPF values approximately equal to .01, .03 and .05. Matteo Masotti. June 1, 2005 – PhD Defense.

(99) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Flow Diagram. Features. The Two Classes Masses Non–masses. 7→. Pixels. 7→. Wavelets Ranklets. Matteo Masotti. June 1, 2005 – PhD Defense. Classifier SVM.

(100) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Motivation. Why ranklet–based image representations?. Matteo Masotti. June 1, 2005 – PhD Defense.

(101) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Motivation. Why ranklet–based image representations? To evaluate whether their non–parametricity improve the discrimination between masses and non–masses. Matteo Masotti. June 1, 2005 – PhD Defense.

(102) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Definition. Ranklets are features modeled on Haar wavelets. Matteo Masotti. June 1, 2005 – PhD Defense.

(103) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Definition. Ranklets are features modeled on Haar wavelets Properties:. Matteo Masotti. June 1, 2005 – PhD Defense.

(104) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Definition. Ranklets are features modeled on Haar wavelets Properties: orientation selective. Matteo Masotti. June 1, 2005 – PhD Defense.

(105) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Definition. Ranklets are features modeled on Haar wavelets Properties: orientation selective non–parametric. Matteo Masotti. June 1, 2005 – PhD Defense.

(106) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Definition. Ranklets are features modeled on Haar wavelets Properties: orientation selective non–parametric multi–resolution. Matteo Masotti. June 1, 2005 – PhD Defense.

(107) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Orientation Selective Property The Haar wavelet supports are defined: −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. Horizontal. Matteo Masotti. +1. −1. (T D ). (C D). −1 (C D). +1 (T D ). Diagonal. June 1, 2005 – PhD Defense.

(108) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Orientation Selective Property The Haar wavelet supports are defined: −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. Horizontal. Matteo Masotti. +1. −1. (T D ). (C D). −1 (C D). +1 (T D ). Diagonal. June 1, 2005 – PhD Defense.

(109) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Orientation Selective Property The Haar wavelet supports are defined: −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. Horizontal. +1. −1. (T D ). (C D). −1 (C D). Diagonal. Then:. Matteo Masotti. +1 (T D ). June 1, 2005 – PhD Defense.

(110) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Orientation Selective Property The Haar wavelet supports are defined: −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. Then:. Horizontal. +1. −1. (T D ). (C D). −1 (C D). +1 (T D ). Diagonal. How many pixel pairs (pm , pn ) with pm ∈ Tj and pn ∈ Cj such that Intensity(pm ) > Intensity(pn )? Matteo Masotti. June 1, 2005 – PhD Defense.

(111) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Non–Parametric Property The ranklet coefficients are computed: P Rj =. p∈Tj. RankCj ∪Tj (p) − N2 8. Matteo Masotti. N N 4(2. + 1). − 1,. j = V, H, D. June 1, 2005 – PhD Defense.

(112) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Non–Parametric Property The ranklet coefficients are computed: P Rj =. p∈Tj. RankCj ∪Tj (p) − N2 8. N N 4(2. + 1). − 1,. j = V, H, D. Number of pixel pairs (pm , pn ) ∈ (Tj × Cj ) such that 2 Intensity(pm ) > Intensity(pn ). Possible values ∈ [0, N4 ]. Matteo Masotti. June 1, 2005 – PhD Defense.

(113) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Non–Parametric Property The ranklet coefficients are computed: P Rj =. p∈Tj. RankCj ∪Tj (p) − N2 8. N N 4(2. + 1). − 1,. j = V, H, D. Number of pixel pairs (pm , pn ) ∈ (Tj × Cj ) such that 2 Intensity(pm ) > Intensity(pn ). Possible values ∈ [0, N4 ] Rj ∼ +1 if pixels in Tj have intensity values > than Cj Rj ∼ −1 if pixels in Tj have intensity values < than Cj. Matteo Masotti. June 1, 2005 – PhD Defense.

(114) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Example Synthetic image. RV,H,D = [−0.28, 0, 0]. Matteo Masotti. June 1, 2005 – PhD Defense.

(115) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Example Synthetic image. RV,H,D = [−0.28, 0, 0]. Matteo Masotti. Real image. RV,H,D = [−0.98, −0.08, 0.06]. June 1, 2005 – PhD Defense.

(116) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Multi–Resolution Property The ranklet coefficients can be calculated at different resolutions: Resolution 1: −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. Horizontal. Matteo Masotti. +1. −1. (T D ). (C D). −1 (C D). +1 (T D ). Diagonal. June 1, 2005 – PhD Defense.

(117) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Multi–Resolution Property The ranklet coefficients can be calculated at different resolutions: Resolution 2: −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. −1 (C D). −1 (C D). Horizontal. Matteo Masotti. +1 (T D ). +1 (T D ). Diagonal. June 1, 2005 – PhD Defense.

(118) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Multi–Resolution Property The ranklet coefficients can be calculated at different resolutions: Resolution 2: −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. Horizontal. Matteo Masotti. +1. −1. (T D ). (C D). −1 (C D). +1 (T D ). Diagonal. June 1, 2005 – PhD Defense.

(119) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Multi–Resolution Property The ranklet coefficients can be calculated at different resolutions: Resolution 2: −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. Horizontal. Matteo Masotti. +1. −1. (T D ). (C D). −1 (C D). Diagonal. June 1, 2005 – PhD Defense. +1 (T D ).

(120) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Multi–Resolution Property The ranklet coefficients can be calculated at different resolutions: Resolution 2:. −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. −1 (C D). −1 (C D). Horizontal. Matteo Masotti. +1 (T D ). +1 (T D ). Diagonal. June 1, 2005 – PhD Defense.

(121) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Multi–Resolution Property The ranklet coefficients can be calculated at different resolutions: Resolution 2:. −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. Horizontal. Matteo Masotti. +1. −1. (T D ). (C D). −1 (C D). +1 (T D ). Diagonal. June 1, 2005 – PhD Defense.

(122) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Multi–Resolution Property The ranklet coefficients can be calculated at different resolutions: Resolution 2:. −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. Horizontal. Matteo Masotti. +1. −1. (T D ). (C D). −1 (C D). Diagonal. June 1, 2005 – PhD Defense. +1 (T D ).

(123) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Multi–Resolution Property The ranklet coefficients can be calculated at different resolutions: Resolution 2:. −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. −1 (C D). −1 (C D). Horizontal. Matteo Masotti. +1 (T D ). +1 (T D ). Diagonal. June 1, 2005 – PhD Defense.

(124) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Multi–Resolution Property The ranklet coefficients can be calculated at different resolutions: Resolution 2:. −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. Horizontal. Matteo Masotti. +1. −1. (T D ). (C D). −1 (C D). +1 (T D ). Diagonal. June 1, 2005 – PhD Defense.

(125) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Multi–Resolution Property The ranklet coefficients can be calculated at different resolutions: Resolution 2:. −1. +1. +1. (T H ). (C V). (T V ). −1. (C H). Vertical. Horizontal. Matteo Masotti. +1. −1. (T D ). (C D). −1 (C D). Diagonal. June 1, 2005 – PhD Defense. +1 (T D ).

(126) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Multi–Resolution Property The ranklet coefficients can be calculated at different resolutions: Resolution 3: −1. +1. +1. (TH). (CV). (TV). −1. (CH). Vertical. +1. −1. (TD). (CD). −1 (CD). Horizontal. Matteo Masotti. +1 (TD). Diagonal. June 1, 2005 – PhD Defense.

(127) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – ROC Curve (Varying Kernels) 1 0.9 0.8. True Positive Fraction. 0.7 0.6 0.5 0.4 0.3 0.2. PixHRS with lin. ker. (256 feat.) OwtS2 with pol. ker., degree = 2 (~3000 feat.) RankS at res. [16,8,4,2] with lin. ker. (1428 feat.) RankS at res. [16,8,4,2] with pol. ker., degree = 2 (1428 feat.) RankS at res. [16,8,4,2] with pol. ker., degree = 3 (1428 feat.). 0.1 0. 0. 0.01. 0.02. 0.03. 0.04 0.05 0.06 False Positive Fraction. Matteo Masotti. 0.07. 0.08. June 1, 2005 – PhD Defense. 0.09.

(128) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – ROC Curve (All Resolutions) 1 0.9 0.8. True Positive Fraction. 0.7 0.6 0.5 0.4 0.3 0.2. PixHRS with lin. ker. (256 feat.) OwtS2 with pol. ker., degree = 2 (~3000 feat.) RankS at res. [16,14,12,10,8,6,4,2] with pol. ker., degree = 3 (2040 feat.) RankS at res. [16,8,4,2] with pol. ker., degree = 3 (1428 feat.) RankS at res. [16,8,2] with pol. ker., degree = 3 (921 feat.). 0.1 0. 0. 0.01. 0.02. 0.03. 0.04 0.05 0.06 False Positive Fraction. Matteo Masotti. 0.07. 0.08. June 1, 2005 – PhD Defense. 0.09.

(129) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – ROC Curve (Low + High Resolutions) 1 0.9 0.8. True Positive Fraction. 0.7 0.6 0.5 0.4 0.3 0.2. PixHRS with lin. ker. (256 feat.) OwtS2 with pol. ker., degree = 2 (~3000 feat.) RankS at res. [16,8,4,2] with pol. ker., degree = 3 (1428 feat.) RankS at res. [16,2] with pol. ker., degree = 3 (678 feat.) RankS at res. [16,4] with pol. ker., degree = 3 (510 feat.). 0.1 0. 0. 0.01. 0.02. 0.03. 0.04 0.05 0.06 False Positive Fraction. Matteo Masotti. 0.07. 0.08. June 1, 2005 – PhD Defense. 0.09.

(130) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – ROC Curve (Low + Intermediate Resolutions) 1 0.9 0.8. True Positive Fraction. 0.7 0.6 0.5 0.4 0.3 0.2. PixHRS with lin. ker. (256 feat.) OwtS2 with pol. ker., degree = 2 (~3000 feat.) RankS at res. [16,8,4,2] with pol. ker., degree = 3 (1428 feat.) RankS at res. [16,14,12,10] with pol. ker., degree = 3 (252 feat.) RankS at res. [16,8] with pol. ker., degree = 3 (246 feat.). 0.1 0. 0. 0.01. 0.02. 0.03. 0.04 0.05 0.06 False Positive Fraction. Matteo Masotti. 0.07. 0.08. June 1, 2005 – PhD Defense. 0.09.

(131) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – ROC Curve (Histogram Equalization) 1 0.9 0.8. True Positive Fraction. 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0. RankS at res. [16,8,4,2] with pol. ker., degree = 3, + hist. eq. (1428 feat.) RankS at res. [16,8,4,2] with pol. ker., degree = 3, (1428 feat.). 0. 0.01. 0.02. 0.03. 0.04 0.05 0.06 False Positive Fraction. Matteo Masotti. 0.07. 0.08. June 1, 2005 – PhD Defense. 0.09.

(132) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Some Numerical Results. RankS3 PixHRS OwtS2 DwtHS3. FPF ∼ .01 .76 ± .05 .70 ± .06 .62 ± .11. FPF ∼ .03 .87 ± .05 .84 ± .05 .82 ± .05 .78 ± .04. FPF ∼ .05 .91 ± .04 .89 ± .03 .87 ± .05 .85 ± .03. Table: Classification results comparison. The TPF values obtained by the best performing pixel–based, DWT–based, OWT–based and ranklet–based image representations are shown, in particular for FPF values approximately equal to .01, .03 and .05. Matteo Masotti. June 1, 2005 – PhD Defense.

(133) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Recursive Feature Elimination RFE is a method for eliminating features responsible of small changes in the classifier’s cost function 7→ feature reduction. Matteo Masotti. June 1, 2005 – PhD Defense.

(134) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Recursive Feature Elimination RFE is a method for eliminating features responsible of small changes in the classifier’s cost function 7→ feature reduction SVM’s cost function: 1 J = αT Hα − αT 1, 2. Matteo Masotti. H(i, j) = yi yj K (xi , xj ). June 1, 2005 – PhD Defense.

(135) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Recursive Feature Elimination RFE is a method for eliminating features responsible of small changes in the classifier’s cost function 7→ feature reduction SVM’s cost function: 1 J = αT Hα − αT 1, 2. H(i, j) = yi yj K (xi , xj ). RFE iterative implementation:. Matteo Masotti. June 1, 2005 – PhD Defense.

(136) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Recursive Feature Elimination RFE is a method for eliminating features responsible of small changes in the classifier’s cost function 7→ feature reduction SVM’s cost function: 1 J = αT Hα − αT 1, 2. H(i, j) = yi yj K (xi , xj ). RFE iterative implementation: 1. SVM is trained and tested with the actual set of ranklet coefficients. Matteo Masotti. June 1, 2005 – PhD Defense.

(137) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Recursive Feature Elimination RFE is a method for eliminating features responsible of small changes in the classifier’s cost function 7→ feature reduction SVM’s cost function: 1 J = αT Hα − αT 1, 2. H(i, j) = yi yj K (xi , xj ). RFE iterative implementation: 1. 2. SVM is trained and tested with the actual set of ranklet coefficients the variation ∆J is computed by removing singularly each ranklet coefficient. Matteo Masotti. June 1, 2005 – PhD Defense.

(138) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – Recursive Feature Elimination RFE is a method for eliminating features responsible of small changes in the classifier’s cost function 7→ feature reduction SVM’s cost function: 1 J = αT Hα − αT 1, 2. H(i, j) = yi yj K (xi , xj ). RFE iterative implementation: 1. 2. 3. SVM is trained and tested with the actual set of ranklet coefficients the variation ∆J is computed by removing singularly each ranklet coefficient the ranklet coefficient corresponding to the smallest ∆J is removed Matteo Masotti. June 1, 2005 – PhD Defense.

(139) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE + Cross–Validation. RFE iterative implementation combined to cross–validation:. Matteo Masotti. June 1, 2005 – PhD Defense.

(140) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE + Cross–Validation. RFE iterative implementation combined to cross–validation: 1. Train SVM for each fold. Matteo Masotti. June 1, 2005 – PhD Defense.

(141) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE + Cross–Validation. RFE iterative implementation combined to cross–validation: 1. Train SVM for each fold. 2. Test SVM for each fold. Matteo Masotti. June 1, 2005 – PhD Defense.

(142) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE + Cross–Validation. RFE iterative implementation combined to cross–validation: 1. Train SVM for each fold. 2. Test SVM for each fold. 3. Compute the ranking criterion for each feature in each fold. Matteo Masotti. June 1, 2005 – PhD Defense.

(143) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE + Cross–Validation. RFE iterative implementation combined to cross–validation: 1. Train SVM for each fold. 2. Test SVM for each fold. 3. Compute the ranking criterion for each feature in each fold. 4. Compute a ranking list, common to all folds, by averaging the ranking position of each feature in each fold. Matteo Masotti. June 1, 2005 – PhD Defense.

(144) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE + Cross–Validation. RFE iterative implementation combined to cross–validation: 1. Train SVM for each fold. 2. Test SVM for each fold. 3. Compute the ranking criterion for each feature in each fold. 4. Compute a ranking list, common to all folds, by averaging the ranking position of each feature in each fold. 5. Remove the feature with the smallest rank in the ranking list. Matteo Masotti. June 1, 2005 – PhD Defense.

(145) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (Error). 0.2. 0.3 0.2. 0.1. 0.1. 0.1. 0.1. 0. 0. 0. 0. 500 1000 Features Number FOLD6. 0.5. 0. FOLD7. 0.5. 0.2. 500 1000 Features Number FOLD8. 0.3 0.2. 0.2. 0.1. 0.1. 0.1. 0. 0. 0. 500 1000 Features Number. 0. 500 1000 Features Number. FOLD9. 0. 500 1000 Features Number. Matteo Masotti. 0. 500 1000 Features Number FOLD10. 0.5 0.4. 0.2. 0. 0.2. 0. 500 1000 Features Number. 0.3. 0.1. 0. 0. 0.4. 0.3. 0.3. 0.1. 0.5. 0.4. Classification Error. 0.3. 0. 0.5. 0.4. Classification Error. 0.4. 500 1000 Features Number. Classification Error. 0. 0.4. Classification Error. 0.2. 0.4. 0.3. FOLD5. 0.5. Classification Error. 0.2. 0.3. FOLD4. 0.5. 0.4. Classification Error. 0.3. FOLD3. 0.5. 0.4. Classification Error. Classification Error. 0.4. Classification Error. FOLD2. 0.5. Classification Error. FOLD1. 0.5. 0.3 0.2 0.1. 0. 500 1000 Features Number. 0. June 1, 2005 – PhD Defense. 0. 500 1000 Features Number.

(146) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (ROC Curve) 0.9. True Positive Fraction. 0.85. 0.8. 0.75. 0.7. 0.65. 0.6 0.005. RankS at res. [16,8,4,2] with pol. ker., degree = 3 (1428 feat.) RankS at res. [16,8,4,2] with pol. ker., degree = 3 (1000 selected feat.) RankS at res. [16,8,4,2] with pol. ker., degree = 3 (200 selected feat.). 0.01. 0.015. 0.02 0.025 0.03 False Positive Fraction. Matteo Masotti. 0.035. 0.04. June 1, 2005 – PhD Defense. 0.045.

(147) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (500 Most Important Ranklet Coeffs) Reducing the number of ranklet coefficients from 1428 to 500 by means of RFE: Resolution16x16 0. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. Resolution8x8 10. 11. 12. 13. 14. 15. 16. 0. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. Resolution4x4 10. 11. 12. 13. 14. 15. 16. 0. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. Resolution2x2 10. 11. 12. 13. 14. 15. 16. 0. 1. 1. 1. 1. 2. 2. 2. 2. 3. 3. 3. 3. 4. 4. 4. 4. 5. 5. 5. 5. 6. 6. 6. 6. 7. 7. 7. 8. 8. 8. 9. 9. 9. 9. 10. 10. 10. 10. 11. 11. 11. 11. 12. 12. 12. 12. 13. 13. 13. 13. 14. 14. 14. 14. 15. 15. 15. 15. 16. 16. 16. 16. Res. 16 × 16. Res. 8 × 8. Matteo Masotti. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 7 8. Res. 4 × 4. June 1, 2005 – PhD Defense. Res. 2 × 2. 14. 15. 16.

(148) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (300 Most Important Ranklet Coeffs) Reducing the number of ranklet coefficients from 1428 to 300 by means of RFE: Resolution16x16 0. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. Resolution8x8 10. 11. 12. 13. 14. 15. 16. 0. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. Resolution4x4 10. 11. 12. 13. 14. 15. 16. 0. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. Resolution2x2. 10. 11. 12. 13. 14. 15. 16. 0. 1. 1. 1. 1. 2. 2. 2. 2. 3. 3. 3. 3. 4. 4. 4. 4. 5. 5. 5. 5. 6. 6. 6. 6. 7. 7. 7. 8. 8. 8. 9. 9. 9. 9. 10. 10. 10. 10. 11. 11. 11. 11. 12. 12. 12. 12. 13. 13. 13. 13. 14. 14. 14. 14. 15. 15. 15. 15. 16. 16. 16. 16. Res. 16 × 16. Res. 8 × 8. Matteo Masotti. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 7 8. Res. 4 × 4. June 1, 2005 – PhD Defense. Res. 2 × 2. 14. 15. 16.

(149) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (200 Most Important Ranklet Coeffs) Reducing the number of ranklet coefficients from 1428 to 200 by means of RFE: Resolution16x16 0. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. Resolution8x8 10. 11. 12. 13. 14. 15. 16. 0. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. Resolution4x4. 10. 11. 12. 13. 14. 15. 16. 0. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. Resolution2x2 10. 11. 12. 13. 14. 15. 16. 0. 1. 1. 1. 1. 2. 2. 2. 2. 3. 3. 3. 3. 4. 4. 4. 4. 5. 5. 5. 5. 6. 6. 6. 6. 7. 7. 7. 8. 8. 8. 9. 9. 9. 9. 10. 10. 10. 10. 11. 11. 11. 11. 12. 12. 12. 12. 13. 13. 13. 13. 14. 14. 14. 14. 15. 15. 15. 15. 16. 16. 16. 16. Res. 16 × 16. Res. 8 × 8. Matteo Masotti. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 7 8. Res. 4 × 4. June 1, 2005 – PhD Defense. Res. 2 × 2. 14. 15. 16.

(150) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (Considerations) Some considerations can be drawn:. Matteo Masotti. June 1, 2005 – PhD Defense.

(151) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (Considerations) Some considerations can be drawn: At resolutions 2 × 2 and 4 × 4:. Matteo Masotti. June 1, 2005 – PhD Defense.

(152) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (Considerations) Some considerations can be drawn: At resolutions 2 × 2 and 4 × 4: surviving ranklet coefficients are near the borders of the crop. Matteo Masotti. June 1, 2005 – PhD Defense.

(153) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (Considerations) Some considerations can be drawn: At resolutions 2 × 2 and 4 × 4: surviving ranklet coefficients are near the borders of the crop masses 7→ sharp edges near the borders of the crop. Matteo Masotti. June 1, 2005 – PhD Defense.

(154) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (Considerations) Some considerations can be drawn: At resolutions 2 × 2 and 4 × 4: surviving ranklet coefficients are near the borders of the crop masses 7→ sharp edges near the borders of the crop non–masses 7→ has not. Matteo Masotti. June 1, 2005 – PhD Defense.

(155) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (Considerations) Some considerations can be drawn: At resolutions 2 × 2 and 4 × 4: surviving ranklet coefficients are near the borders of the crop masses 7→ sharp edges near the borders of the crop non–masses 7→ has not. At resolutions 8 × 8 and 16 × 16:. Matteo Masotti. June 1, 2005 – PhD Defense.

(156) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (Considerations) Some considerations can be drawn: At resolutions 2 × 2 and 4 × 4: surviving ranklet coefficients are near the borders of the crop masses 7→ sharp edges near the borders of the crop non–masses 7→ has not. At resolutions 8 × 8 and 16 × 16: surviving ranklet coefficients are near the center of the crop. Matteo Masotti. June 1, 2005 – PhD Defense.

(157) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (Considerations) Some considerations can be drawn: At resolutions 2 × 2 and 4 × 4: surviving ranklet coefficients are near the borders of the crop masses 7→ sharp edges near the borders of the crop non–masses 7→ has not. At resolutions 8 × 8 and 16 × 16: surviving ranklet coefficients are near the center of the crop masses 7→ quite symmetric structure. Matteo Masotti. June 1, 2005 – PhD Defense.

(158) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview Pixels Wavelets Ranklets. Ranklets – RFE (Considerations) Some considerations can be drawn: At resolutions 2 × 2 and 4 × 4: surviving ranklet coefficients are near the borders of the crop masses 7→ sharp edges near the borders of the crop non–masses 7→ has not. At resolutions 8 × 8 and 16 × 16: surviving ranklet coefficients are near the center of the crop masses 7→ quite symmetric structure non–masses 7→ less definite structure. Matteo Masotti. June 1, 2005 – PhD Defense.

(159) Digital Mammography Two–Class Pattern Classification Exploring Image Representations CAD System Implementation Summary. Overview CAD Scheme Results. Outline. 1. Digital Mammography. 2. Two–Class Pattern Classification. 3. Exploring Image Representations. 4. CAD System Implementation. Matteo Masotti. June 1, 2005 – PhD Defense.