Midterm Review

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 (contd)

• 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 (contd)

• 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 (contd)

• 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

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Edge Detection (contd)

• Edge detection using derivatives
• First derivative for edge detection
• Min/Max why?
• Second derivative for edge detection
• Zero crossings why?

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Edge Detection (contd)

• 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 (contd)

• 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 (contd)

• Laplacian edge detector
• Properties
• Comparison with gradient magnitude
• Laplacian of Gaussian (LoG) edge detector
• Decomposition using 1D convolutions
• Difference of Gaussians (DoG)

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Edge Detection (contd)

• 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 (contd)

• Anisotropic filtering
• Main idea and implications
• Multi-scale edge detection
• Effect of s
• Multiple scales
• Interesting scales
• Coarse-to-fine edge localization

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Math Review - Vectors

• Dot product and geometric interpretation
• Orthogonal/Orthonormal vectors
• Linear combination of vectors
• Space spanning
• Linear independence/dependence
• Vector basis
• Vector expansion

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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

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Math Review Solving Ax b

• Overdetermined/Underdetermined systems
• Conditions for solutions of Axb
• One solution
• Multiple solutions
• No solution
• Conditions for solutions of Ax0
• Trivial and non-trivial solutions

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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 Axb using SVD
• Over-determined systems (mgtn)
• Homogeneous systems (b0)

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

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Interest Points Detection (contd)

• Moravec detector
• Main steps
• Strengths and weaknesses

23
Interest Points Detection (contd)

• 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 (contd)

• 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 (contd)

• Using LoG for automatic scale selection
• How are the characteristic scale and spatial
  extent being determined using LoG?
• How and why do we normalized LoGs response?
• Harris-Laplace detector
• Main steps
• Implement Harris-Laplace using DoG
• Strengths and weaknesses

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Interest Points Detection (contd)

• 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 (contd)

• 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