Vectors — notation?
Bold lowercase letters, e.g., v.
Matrices — notation?
Bold uppercase letters, e.g., A.
Complex conjugation — symbol?
Asterisk (*).
Hadamard product — meaning?
Element-wise multiplication.
Image function — domain?
Spatial coordinates Ω.
Discrete images — representation?
Pixel grid as matrices or arrays.
Coordinate system — origin?
Typically at upper-left pixel.
Visualization methods?
Matrix view, color image, surface, profile.
Discretization — steps?
Sampling (domain), quantization (range).
Interpolation — purpose?
Estimate pixel values at non-grid points.
Linear transformation — property?
Preserves addition and scalar multiplication.
Shift invariance — property?
Response independent of position.
Affine transformation — components?
Linear + translation.
Image resolution — determines?
Detail level and spatial clarity.
Contrast — formula?
(Imax - Imin)/(Imax + Imin).
Noise — model?
Additive random component.
Memory footprint — calculation?
Width × Height × bits per pixel.
Coordinate transformation — role?
Convert pixel to physical coordinates.
Surface plot — shows?
Intensity as height in 3D.
Separable kernel — advantage?
Reduced computation via 1D operations.
Homogeneous coordinates — use?
Represent affine transforms as matrices.
Geometric transformation — example?
Rotation, scaling, translation.
Image characteristics — include?
Resolution, contrast, noise, size.
Test your knowledge with 12 questions on Fundamentals of Image Processing and Transformations.
1. In the context of mathematical notation in image processing, what does the symbol '*' represent when applied to vectors or matrices?
2. In the typical coordinate system used in image processing, where is the origin located and how are the axes oriented?
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