Course Syllabus and Schedule: CS673 (Spring 1998)

Computational Vision

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Lecture 2

2.1 Introduction to Computer Vision

2.1.1 Sensors

2.1.2 1-D Seneor Arrays

2.2 Sampling and Quantization

2.2.1 Spatial Resolution

2.2.2 Image Resolution

2.3 Computer Vision Algorithm

2.4 Role of Knowledge

2.4.1 Domain Specific Knowledge

2.4.2 General Knowledge

2.5 Levels of Computation

2.5.1 Point Level

2.5.2 Local Level

2.5.3 Global Level

2.5.4 Object Level

Lecture 3

3.1 Image Formation

3.1.1 Three classes of imaging system

3.1.1.1 Perspective projection

3.1.1.2 Orthographic projection

3.1.1.3 Lenses

3.2 Brightness

3.2.1 Image Brightness

3.2.2 Scene Brightness

3.3 Properties of Scene in Our Universe

3.3.1 Objects usually opaque

3.3.2 Medium for light rays

3.3.3 Surfaces are two-dimensional

3.4 lDepth of Field

3.5 View Volume

Lecture 4

4.1 Image Acquisition

4.1.1 Structed Lighting

4.1.2 Image Detection

4.1.2.1 Tube Cameras

4.1.2.1 Vacuum Tubes

4.1.2.2 Older Technologies

4.1.2.3 TV Cameras

4.1.2.4 Higher Resolution

4.1.2.5 Color Quality

4.1.2.6 Low Light Intensity Senesitivity

4.2. Solid State Cameras

4.2.1 Two-Dimensional Sensor Arrays

4.2.2 One-Dimensional Sensor Arrays

Lecture 5

5.1. Binary Images

5.1.1 Continuous Binary Images

5.1.2 Discrete Binary Images

5.1.2.1 Thresholding and Segmentation

Lecture 6

6.1 Binary Algorithms

6.1.1 Basic Definition

6.1.1.1 Neighbors

6.1.1.2 Path

6.2 Local Counting

6.2.1 Global Operations

6.2.2 Local Operations

6.3 Connectivity

6.3.1 Reflexivity

6.3.2 Commutivity

6.3.3 Transitivity

6.4 Compactness

6.4.1 What shape is most compact?

6.4.2 What value will the computer have for that shape?

6.4.3 What class of shapes will be least compact?

6.5 Distance Measures

6.5.1 Euclidean

6.5.2 City-Block metric

6.5.3 Chessboard metric

6.6 Euler Number

6.6.1 Topological property

6.7 Iterative Modification

6.8 Skeleton Transformation

6.8.1 SAT(Symmetric Axis Transform)

6.8.2 SLS(Smoothed Local Symmetries)

6.8.3 PISA(Process Inferring Symmetry Axes)

Lecture 7

7.1 Mathematical Morphology

7.1.1 Minkowski Addition

7.1.2 Minkowski Subtraction

7.2 Erosion

7.2.1 Shrinks and Translates

7.3 Dilation

7.3.1 Expands and Translates

7.4 Noise Reduction using Mathematical Morphology

Lecture 8

8.1 Segmentation

8.1.1 How to determine what is a region?

8.1.1.1 Uniform intensity or color

8.1.1.2 Uniform Texture

8.1.1.3 Bounded by Edges

8.1.1.4 Uniform Motion

8.2 Possible Solution for Multiple Regions

8.2.1 Multidimensional Histograming

8.2.1 Multispectral Histograming

Lecture 9

9.1 Segmentation Continued

9.1.1 Interactive vs Automatic Thresholding

9.1.2 Mode Method

9.1.3 Iterative Threshold Selection

9.1.4 Adaptive Thresholding

9.1.5 Variable Thresholding

9.1.5 Double Thresholding

9.1.5.1 Finding three regions

9.1.5.1.1 R1 contains only object pixels

9.1.5.1.2 R2 contains object and background pixels

9.1.5.1.3 R3 contains only background pixels

9.2 Split and Merge

9.2.1 Horowitz and Pavlidis

9.3 Representing Regions

9.3.1 Array Representation

9.3.1.1 Single 2D array

9.3.1.2 Multiple 2D arrays membership images, masks, bitmaps

9.4 Symbolic Representation

9.4.1 Bounding Box

9.4.2 Centroid

9.4.3 Moments

9.4.4 Euler Number

9.4.5 Compactness

9.4 Data Structure for Segmentation

9.4.1 Region Adjacency Graphs

9.4.1.1 Nodes

9.4.1.2 Arcs

9.4.2 Picture Tress

9.5 Super Grid

9.6 Removing Weak Edges

Lecture 10

10.1 Continuous Image Processing

10.1.1 Linear System

10.1.2 Shift Invariant

10.1.3 Convolution

10.1.3.1 Sifting Properrty

10.1.4 Impulse Response of One-Dimensional Linear Shift Invariant System

10.1.5 Point Spread Function

10.1.6 Properties of Convolution

10.1.6.1 Commutivity

10.1.6.2 Associativity

10.1.7 Convolution and the Frequency Domain

10.1.7.1 1-D Signal Processing

10.1.7.2 2-D Image Processing

10.1.8 Two-Dimensional Fourier Transform Pairs

10.1.8.1 Image

10.1.8.2 Magnitude Fourier Spectrum

10.1.8.3 Frequency Content of Images

10.1.8.3.1 Low Frequency Components

10.1.8.3.2 High Frequency Components

10.1.8.4 Filtering in the frequency domain

10.1.8.4.1 Low-pass filtering

10.1.8.4.2 High-pass filtering

10.1.8.4.3 Band-pass filtering

10.1.8.4.4 Gaussian filtering

10.1.9 Discrete Images

10.1.10 Edge Effects

10.1.10.1 Bandlimiting

10.1.10.1.1 Sensors

10.1.10.1.2 Optics

Lecture 11

11.1 Edge Detection

11.1.1 Two Goals

11.1.1.1 Find Location of intensity edges

11.1.1.2 Find Orientation of intensity edges

11.1.2 Classes of Edge Dectectors

11.1.2.1 Gradiant operators

11.1.2.2 Compass operators

11.1.2.3 Laplace operators

11.1.2.4 Stochastic gradiants

11.1.3 Functioning of Robert's operator

Lecture 12

12.1 Edge Detection Continued

12.1.1 Canny Operator

12.1.1.1 Type of compass operator and designed to satisfy three criteria

12.1.1.1.1 Good Detection

12.1.1.1.2 Good Localization

12.1.1.1.3 Only one response to a single edge

12.1.2 Witkin's Scale Space Filtering

12.1.2.1 Convolve with Gaussian

12.1.2.2 Find edges- Laplacian

12.1.3 Properties of Marr-Hildreth operator

12.1.4 Idea of Scale Space

12.1.5 How tomeasure edge detection performance

Lecture 13

13.1 Contours

13.1.1 Contour Images

13.1.1.1 Criteria for Contour representation

13.1.1.2 Two types of curve fitting

13.1.1.2.1 Interpolation

13.1.1.2.2 Approximation

13.1.2 Planar Curve Representation

13.1.2.1 Explicit

13.1.2.2 Implicit

13.1.2.3 Parametric

13.1.2.4 Unit Tagent Vector

13.1.3 Digital Curves

13.1.4 Chain Codes

13.1.5 Slope-Density Functions

13.1.6 Curve Fitting

13.1.7 How to model edge points using line segments?

13.1.7.1 Segment Merging

Lecture 14

14.1 Hough Transform

14.1.1 Local edge linking algorithms

14.1.2 Hough Transform

14.1.3 Rosenfeld

14.1.4 Hough Transform for a Circle

14.1.5 Fourier Desriptors

Lecture 15

15.1 Texture

15.1.1 Segmentation

15.1.2 Texture Identification

15.1.3 Texture Description

15.1.4 Different Approaches to Computer Vision

15.1.4.1 Machine Vision

15.1.4.2 Computational Vision

15.1.5 Grey-level Co-Occurance

15.1.6 Mathematical Morphology

15.1.6.1 Binary Images

15.1.7 Texton Theory

15.1.8 Develop analytical model of texture

15.1.8.1 Fourier model

15.1.8.2 Markov Random Field Model

15.1.8.3 Fractal Based Model

15.1.9 Shape from texture

Lecture 16

16.1. Reflectance Maps and Photometric Stereo

16.1.1 Scene Brightness from Image Brightness

16.1.2 Surface Orientation from Image Brightness

16.1.3 Light Reaching the Lens

16.1.4 Energy Reaching the Image Patch

16.2 The perspective transformation

16.2.1 Bidirectional Distribution Function

16.2.2 Surface Reflectance Properties

16.3 Reflectance Map

Lecture 17

17.1 Shape From Shading

17.1.1 Photometric Stereo

17.1.2 Shape From Shading for Linear Reflectance Map

Lecture 18

18.1 Color and Brightness

18.1.1 Monchromatic Light

18.1.2 Simple Correlation between Wavelength and Color

18.2 Colors are Cognitive Concepts

18.2.1 Perceptual Color Space

18.2.1.1 Brightness

18.2.1.2 Hue

18.2.1.3 Saturation

18.3 Lands Retirex Theory

18.4 Color Constancy

18.4.1 Spectural Distribution

Lecture 19

19.1 Stereo

19.1.1 Relative Depth

19.1.2 Absolute 3-D Coordinates

19.2 Stereo Geometry

19.2.1 Random-Dot Stereograms

19.3 Stereo Matching Algorithm for 1-D Binary Images

19.4 Range Images

Lecture 20

20.1 Calibration - Photogrammetry

20.1.1 Four Basic problems

20.1.1.1 Absolute orientation

20.1.1.2 Relative orientation

20.1.1.3 Exterior orientation

20.1.1.4 Interior orientation

20.1.2 Coordinate System

20.1.3 How do image to scene transformation?

20.1.4 Rigid Body Transformations

20.1.5 How to represent rotation?

20.1.5.1 Euler angles

20.1.5.2 Rotation Matrix

20.1.5.3 Axis of rotation

20.1.5.4 Unit Quaternions

Lecture 21

21.1 Curves and Surfaces

21.1.1 Shape-based Object Recognition

21.1.2 Fields

21.1.2.1 Uniform

21.1.2.2 Rectilinear

21.1.2.3 Irregular

21.1.3 Geometry of Curves

21.1.3.1 Implicit

21.1.3.2 Explicit

21.1.3.3 Parametric

21.1.4 Geometry of Surfaces

21.1.4.1 Implicit

21.1.4.2 Explicit

21.1.4.3 Parametric

21.1.5 Differential Geometry

21.1.6 Curve Representations

21.1.6.1 Cubic Spline Curves

21.1.7 Surface Representations

21.1.7.1 Polygonal Meshes

Lecture 22

22.1 Curves And Surfaces, Continued

22.1.1 Surface Patches

22.1.1.1 Bivariate Polynomials

22.1.1.1.1 Bilinear patches

22.1.1.1.2 Biquadratic patches

22.1.1.1.3 Bicubic patches

22.1.1.1.4 Biquadratic patches

22.2 Tensor-Product Surfaces

22.2.1 Parametric cubix polynomial curve

22.3 Surface Interpolation

22.3.1 Triangular Mesh Interpolation

22.4 Surface Approximation

22.4.1 Surface fitting

22.4.2 How to do Surface Approximation

22.5 Regression Splines

22.5.1 B-Splines

22.6 Surface Segmentation

Lecture 23

23.1 Motion and Optic

23.1.1 Simple Scheme For Motion Detection(1-D)

23.1.2 Optic Flow and Motion Flow

23.1.2.1 Motion Fields

23.1.2.2 Optic Flow-apparent Motion of Brightness Pattern

Lecture 24

24.1 How is the Optical Field Computed?

24.1.1 The Optical Flow Constraint Equation

24.1.2 Finding the Constraint Line

Lecture 25

25.1 Object Recognition

25.1.1 System Components

25.1.1.1 Model Database

25.1.1.2 Feature Detector

25.1.1.3 Hypothesizer

25.1.1.4 Hypothesis Verifier

25.1.2 Object Representaions

25.1.2.1 Constructive Solid Geometry

25.1.3 Spatial Occupancy

25.1.4 Multiple Representation

25.1.5 Surface Boundary Representation

25.1.6 Extended Gaussian Image

25.1.7 Pattern Classification

25.1.7.1 Scene analysis

25.1.7.2 Object recognition

25.1.8 Basic idea of Pattern Classification

25.1.8.1 Nearest Neighbor Classification

25.1.8.2 K Nearest Neighbor Classification

25.1.8.3 Nearest Centroid Classification

25.1.8.4 Use of Probability Density Models

Lecture 26

26.1 Object Recognition, Continued

26.1.1 Neural Networks

26.1.1.1 The Perceptron - Rosenblatt - Calspan

26.1.2 Least Mean Square Neural Network

26.1.2.1 Widrow and Hoff

26.1.3 Use of Neural Network in Object Recognition

26.1.4 Polyhedral Scenes

26.1.5 Huffman and Clowes

26.1.6 How to determine which are the possible labelings for trihedral world?

26.1.7 Geometric Constraints

26.1.8 Use orthogonal constraints to disambiguate drawings

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