Image Processing Toolbox

Linear Filtering and Filter Design

Overview

The Image Processing Toolbox provides a number of functions for designing and implementing two-dimensional linear filters for image data. This chapter describes these functions and how to use them effectively.

The material in this chapter is divided into two parts:

The first part is an explanation of linear filtering and how it is implemented in the toolbox. This topic describes filtering in terms of the spatial domain, and is accessible to anyone doing image processing.

The second part is a discussion about designing two-dimensional finite infinite response (FIR) filters. This section assumes you are familiar with working in the frequency domain.

Words You Need to Know

An understanding of the following terms will help you to use this chapter. For more explanation of this table and others like it, see Words You Need to Know in the Preface. 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 Guide.

Words
Definitions

Computational molecule
A filter matrix used to perform correlation. The filter design functions in the Image Processing Toolbox return computational molecules. A computational molecule is a convolution kernel that has been rotated 180 degrees.

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 filter matrix used to perform convolution. A convolution kernel is a computational molecule 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 computational molecule. Image processing operations implemented with convolution include smoothing, sharpening, and edge enhancement. Correlation is closely related mathematically to convolution.

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.

Separable filter
A two-dimensional filter that can be implemented by a sequence of two one-dimensional filters. Separable filters can be implemented much faster than nonseparable filters. The function filter2 checks a filter for separability before applying it to an image.

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.

Words	Definitions
Computational molecule	A filter matrix used to perform correlation. The filter design functions in the Image Processing Toolbox return computational molecules. A computational molecule is a convolution kernel that has been rotated 180 degrees.
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 filter matrix used to perform convolution. A convolution kernel is a computational molecule 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 computational molecule. Image processing operations implemented with convolution include smoothing, sharpening, and edge enhancement. Correlation is closely related mathematically to convolution.
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.
Separable filter	A two-dimensional filter that can be implemented by a sequence of two one-dimensional filters. Separable filters can be implemented much faster than nonseparable filters. The function `filter2` checks a filter for separability before applying it to an image.
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.

Distinct Blocks Linear Filtering