Midterm Review CS485/685 Computer Vision Prof. Bebis

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

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

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

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

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

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)

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

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

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

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

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

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)

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

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

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

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

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

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)

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

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

Interest Points Detection (cont’d) Moravec detector –Main steps –Strengths and weaknesses

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

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

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

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

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