Linear Filtering and Filter Design (Image Processing Toolbox)

Image Processing Toolbox

Terminology

An understanding of the following terms will help you to use this chapter. Note that this table includes brief definitions of terms related to filter design; a detailed discussion of these terms and the theory behind filter design is outside the scope of this User's Guide.

Terms
Definitions

Convolution
A neighborhood operation in which each output pixel is a weighted sum of neighboring input pixels. The weights are defined by the convolution kernel. Image processing operations implemented with convolution include smoothing, sharpening, and edge enhancement.

Convolution kernel
A matrix of weights used to perform convolution. A convolution kernel is a correlation kernel that has been rotated 180 degrees.

Correlation
A neighborhood operation in which each output pixel is a weighted sum of neighboring input pixels. The weights are defined by the correlation kernel. Correlation is closely related mathematically to convolution.

Correlation kernel
A matrix of weights used to perform correlation. The filter design functions in the Image Processing Toolbox return correlation kernels. A correlation kernel is a convolution kernel that has been rotated 180 degrees.

FIR filter
A filter whose response to a single point, or impulse, has finite extent. FIR stands for finite impulse response. An FIR filter can be implemented using convolution. All filter design functions in the Image Processing Toolbox return FIR filters.

Frequency response
A mathematical function describing the gain of a filter in response to different input frequencies.

Neighborhood operation
An operation in which each output pixel is computed from a set of neighboring input pixels. Convolution, dilation, and median filtering are examples of neighborhood operations.

Ripples
Oscillations around a constant value. The frequency response of a practical filter often has ripples where the frequency response of an ideal filter is flat.

Window method
A filter design method that multiples the ideal impulse response by a window function, which tapers the ideal impulse response. The resulting filter's frequency response approximates a desired frequency response.

Terms	Definitions
Convolution	A neighborhood operation in which each output pixel is a weighted sum of neighboring input pixels. The weights are defined by the convolution kernel. Image processing operations implemented with convolution include smoothing, sharpening, and edge enhancement.
Convolution kernel	A matrix of weights used to perform convolution. A convolution kernel is a correlation kernel that has been rotated 180 degrees.
Correlation	A neighborhood operation in which each output pixel is a weighted sum of neighboring input pixels. The weights are defined by the correlation kernel. Correlation is closely related mathematically to convolution.
Correlation kernel	A matrix of weights used to perform correlation. The filter design functions in the Image Processing Toolbox return correlation kernels. A correlation kernel is a convolution kernel that has been rotated 180 degrees.
FIR filter	A filter whose response to a single point, or impulse, has finite extent. FIR stands for finite impulse response. An FIR filter can be implemented using convolution. All filter design functions in the Image Processing Toolbox return FIR filters.
Frequency response	A mathematical function describing the gain of a filter in response to different input frequencies.
Neighborhood operation	An operation in which each output pixel is computed from a set of neighboring input pixels. Convolution, dilation, and median filtering are examples of neighborhood operations.
Ripples	Oscillations around a constant value. The frequency response of a practical filter often has ripples where the frequency response of an ideal filter is flat.
Window method	A filter design method that multiples the ideal impulse response by a window function, which tapers the ideal impulse response. The resulting filter's frequency response approximates a desired frequency response.

Linear Filtering and Filter Design Linear Filtering