CH3 CHaracterization of discrete image and linear filtering Flashcards
The complex sinusoid form an _ _ of L2 wit respect to the Hermitian product.
orthonormal basis
ROC
Region of C where A(z) converge uniformly
Impulse response =
Space-reversed version of the mask
Orientation-sensitive filters are in general
Non-separable
Filtering:
Periodization, pro and cons
+ simple to implement
+Consistent, filtering of a periodic signal produce a periodic signal
- Produce boundary artifacts
Filtering:
Symmetrization/mirror folding, pro and cons
+Consistent, symmetric filtering of a folded signal produce a folded signal; antisymmetric filtering yields an antisymmetric signal extension
Long filter should be implemented in the
Fourier domain
Most usual image-processing filters are short (3x3) and are implemented most efficiently in the
Space domain
Boundary conditions are handled best in the
Spatial domain
Gaussian filter motivation:
+ Only filter both circular-symmetric and separable
+ Optimal space-frequency localization
Discrete images are sequences indexed by two spatial integer variables. When they have finite energy, they can be viewed as points in the
Hilbert space l_2 (Z^d)
A discrete image is characterized by its 2D Fourier transform which is _-periodic
2pi
Digital filtering can be described as a _ _ _ (running inner product, or as a _ _.
Local masking operation
discrete convolution
A 2D digital filter is either described by a _ (which display the reversed version of the _ _), its _ _, or its frequency response
Mask
impulse response
Transfer function
Many popular image-processing filter are _ and_.
Computations are usually performed in the _ _ by successive filtering along the row and columns
Short and separable
Spatial domain
