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 2 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