MAL

Description

Performs an orthogonal 2-dimensional wavelet transformation on an image channel. The result is a set of detail images at different scales. These images contain horizontal, vertical, or diagonal details in the image within a spatial frequency band.

Parameters

Name	Type	Length	Value range
Input: Input raster channel *	Raster port	1 - 1
Output: Output raster channel(s) *	Raster port	1 - 1024
Report	String	0 - 192	See parameter description

* Required parameter

Parameter descriptions

Input: Input raster channel

Specifies the input raster channel holding the image to process. Only one input channel may be specified.

Output: Output raster channel(s)

Specifies the output image channels in the output file (FILO) to receive the output wavelet detail maps.

Report

Specifies where to direct the generated report.

Available options are:

• LOG: generates a report on the terminal (default)
• <modulename.RPT>: appends a report to the module's RPT file
• DISK: generates a report on file "IMPRPT.LST"

Details

MAL performs an orthogonal 2-dimensional wavelet transformation on a specified image channel. The result is a set of detail images at different scales. These images contain horizontal, vertical, or diagonal details in the image within a spatial frequency band.

The wavelet transformation breaks down the input image into a set of detail images. Each detail image contains the image content within a specific region in spatial frequency, scale space, and orientation. In addition, the bases of generated detail images are mutually orthogonal.

The number of detail images from a complete Mallat wavelet transformation depends on the size of the input image. Detail images occur in groups of three in a succession of decreasing spatial sizes and correspondingly increasing higher-spatial frequency bands. Given an initial image of P pixels and L lines, the first group of three detail images will be of size P/2 pixels and L/2 lines. The second group will be of size P/4 pixels and L/4 lines; the Nth group will be of size P/(2^N) pixels and L/(2^N) lines. The transformation is completed when the size of the next group of detail images would be below 8 pixels or lines. The 8 pixels and lines limit is required to support the filter masks.

Within each group of three detail images, the first computed image contains image information with spatial frequency energy oriented in the vertical direction; the second detail image represents the horizontal spatial frequency information, while the third detail image contains the diagonal spatial frequency information.

The detail images generated using MAL can be though of as a set of multi-scale texture maps. These texture maps can be used by the AVG aggregation neural network to segment a multispectral version of the image used with MAL. Keep in mind that the largest detail image is actually half the pixel and line size of the input image; therefore, when AVG is used, the input multispectral image should also be subsampled by two along rows and columns to match the MAL texture maps. Refer to AVG for an explanation of how MAL or other texture maps are integrated into the neural network.

References

Mallat, S. (1990). Multiscale Image Analysis

Mallat, S. (1989). "A Theory of Multiresolution Signal Decomposition: the Wavelet Representation." IEEE Trans. PAMI, Vol. II, No. 7, pp. 572-693.