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)

2

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