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Midterm Review

This review covers the basics of computer vision, including image formation and representation, image filtering techniques, and edge detection methods. It also includes a math review of vectors, matrices, and geometric transformations.

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Midterm Review

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  1. Midterm Review CS485/685 Computer Vision Prof. Bebis

  2. Midterm Material • Intro to Computer Vision • Image Formation and Representation • Image Filtering • Edge Detection • Math Review • Interest Point Detection

  3. Intro to Computer Vision • What is Computer Vision? • Relation to other fields • Main challenges • Three processing levels: low/mid/high • The role of various visual cues • Applications

  4. Image Formation and Representation • Image formation (i.e., geometry + light) • Pinhole camera model • Effect of aperture size (blurring, diffraction) • Lens, properties of thin lens, thin lens equation • Focal length, focal plane, image plane, focus/defocus (circle of confusion) • Depth of field, relation to aperture size • Field of view, relation to focal length

  5. Image Formation and Representation (cont’d) • Lens flaws (chromatic aberration, radial distortion, tangential distortion) • Human eye (focusing, rods, cones) • Digital cameras (CCD/CMOS) – similarities and differences. • Image digitization (sampling, quantization) and representation • Color sensing (color filter array, demosaicing, color spaces, color processing) • Image file formats

  6. Image Filtering • Point/Area processing methods • Area processing methods using masks - how do we choose and normalize the mask weights? • Correlation • Definition and geometric interpretation using dot product • Convolution • Definition and similarities/differences with correlation

  7. Image Filtering (cont’d) • Smoothing • Goal? Mask weights? • Effect of mask size? • Properties of Gaussian filter • Convolution with self  Gaussian width – proof (grad Students) • Separability property and implications – proof (all)

  8. Image Filtering (cont’d) • Sharpening • Goal? Mask weights? • Effect of mask size?

  9. Edge Detection • What is an edge? What causes intensity changes? • Edge descriptors (i.e., direction, strength, position) • Edge models (step, ramp, ridge, roof) • Mains steps in edge detection • Smoothing, Enhancement, Theresholding, Localization

  10. Edge Detection (cont’d) • Edge detection using derivatives: • First derivative for edge detection • Min/Max – why? • Second derivative for edge detection • Zero crossings – why?

  11. Edge Detection (cont’d) • Edge detection masks by discrete gradient approximations (e.g., Robert, Sobel, Prewitt) – study derivations. • Gradient magnitude and direction • What information do they carry? • Isotropic property of gradient magnitude • Practical issues in edge detection • Noise suppression-localization tradeoff • Thresholding • Edge thinning and linking

  12. Edge Detection (cont’d) • Criteria for optimal edge detection • Good detection/localization, single response. • Canny edge detector • What optimality criteria does it satisfy? • Steps and importance of each step • Main parameters

  13. Edge Detection (cont’d) • Laplacian edge detector • Properties • Comparison with gradient magnitude • Laplacian of Gaussian (LoG) edge detector • Decomposition using 1D convolutions • Difference of Gaussians (DoG)

  14. Edge Detection (cont’d) • Second directional derivative edge detector. • Definition, properties • Comparison with LOG • Facet Model • Main idea – how is it different from traditional edge detection methods? • Steps and implementation details

  15. Edge Detection (cont’d) • Anisotropic filtering • Main idea and implications • Multi-scale edge detection • Effect of σ • Multiple scales • “Interesting” scales • Coarse-to-fine edge localization

  16. Math Review - Vectors • Dot product and geometric interpretation • Orthogonal/Orthonormal vectors • Linear combination of vectors • Space spanning • Linear independence/dependence • Vector basis • Vector expansion

  17. Math Review - Matrices • Transpose, symmetry, determinants • Inverse, pseudo-inverse • Matrix trace and rank • Orthogonal/Orthonormal matrices • Eigenvalues/Eigenvectors • Determinant, rank, trace etc. using eigenvalues • Matrix diagonalization and decomposition • Case of symmetric matrices

  18. Math Review – Solving Ax = b • Overdetermined/Underdetermined systems • Conditions for solutions of Ax=b • One solution • Multiple solutions • No solution • Conditions for solutions of Ax=0 • Trivial and non-trivial solutions

  19. Singular Value Decomposition (SVD) • SVD definition and meaning of each matrix involved • Need to remember equations • Use SVD to compute matrix rank, inverse, condition • Solve Ax=b using SVD • Over-determined systems (m>n) • Homogeneous systems (b=0)

  20. 2D and 3D geometric transformations • Translation, rotation, scaling • Need to remember equations • Be careful with 3D transformations • Homogeneous coordinates • Composition of transformations • Be careful about order of transformations! • Rigid, similarity, affine, projective • Change of coordinate systems

  21. Interest Points Detection • Why are they useful? • Characteristics of “good” local features • Local structure of interest points – gradient should vary in more than one directions • Covariance and invariance properties • Corner detection • Main steps • Methods using contour/intensity information

  22. Interest Points Detection (cont’d) • Moravec detector • Main steps • Strengths and weaknesses

  23. Interest Points Detection (cont’d) • Harris detector • How does it improve the Moravec detector? • Derivation of Harris detector – grad students • Auto-correlation matrix • What information does it encode? • Geometric interpretation? • Computation of “cornerness” • Steps and main parameters • Strengths and weaknesses of the Harris derector

  24. Interest Points Detection (cont’d) • Multi-scale Harris detector • Steps and main parameters • Strengths and weaknesses • Characteristic scale and spatial extent of interest points. • Automatic scale selection • Main idea and implementation details • Local measures for automatic scale selection

  25. Interest Points Detection (cont’d) • Using LoG for automatic scale selection • How are the characteristic scale and spatial extent being determined using LoG? • How and why do we normalized LoG’s response? • Harris-Laplace detector • Main steps • Implement Harris-Laplace using DoG • Strengths and weaknesses

  26. Interest Points Detection (cont’d) • Generalize Harris to handle affine transforms, how? • Affine scale space – what is it? • But, it is not practical, so …. • Harris-Affine detector • Main idea, steps and parameters • Strengths and weaknesses • De-skewing corresponding regions and handing rotation ambiguity  grad students

  27. Interest Points Detection (cont’d) • Other methods for extracting affine-invariant regions: • Intensity Extrema-Based Region (IER) • Main idea and steps • Maximally Stable Extremal Regions (MSERs) • Main idea and steps

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