FTF

Description

Converts imagery data from the spatial domain to the two-dimensional frequency domain using either Fourier, Hadamard, Walsh, or Cosine transformations.

Parameters

Name	Type	Length	Value range
Input: Spatial domain channel *	Raster port	1 - 1
Output: Output frequency domain channel(s) *	Raster port	1 - 2
X Offset	Integer	0 - 4
Y Offset	Integer	0 - 4
X Size	Integer	0 - 4
Y Size	Integer	0 - 4
Transformation Type	String	3 - 1	FIR | FMP | WAL | HAD | COS Default: FIR
Report	String	0 - 192	See parameter description

* Required parameter

Parameter descriptions

Input: Spatial domain channel

Specifies the input spatial domain channel to be transformed to the frequency domain. Complex-valued input channels are supported.

Output: Output frequency domain channel(s)

Specifies the output channel(s) to receive the frequency domain channel(s); that is, the 2-D frequency spectrum of the input raster channel.

It is recommended that real-valued input images have their Fourier transforms stored in real-valued output channels, while complex-valued images have their Fourier transforms stored in complex output channels. This ensures that if the frequency images are subsequently filtered in the frequency domain by the FFREQ module with the help of bitmaps, they are processed correctly. Specifically, the bitmaps are symmetrized for real-valued transforms, but used as-is for complex-valued transforms.

X Offset

In conjunction with the Y Offset parameter, specifies the horizontal offset of the raster window that is read from the input image.

X Offset and Y Offset define the upper-left starting pixel coordinates of the window.

If X Offset, Y Offset, X Size, and Y Size are not specified, the entire image is processed by default.

Y Offset

In conjunction with the X Offset parameter, specifies the vertical offset of the raster window that is read from the input image.

X Offset and Y Offset define the upper-left starting pixel coordinates of the window.

If X Offset, Y Offset, X Size, and Y Size are not specified, the entire image is processed by default.

X Size

In conjunction with the Y Size parameter, specifies the size of the raster window that is read from the input image.

X Size is the number of pixels that define the window width.

If X Offset, Y Offset, X Size, and Y Size are not specified, the entire image is processed by default.

Y Size

In conjunction with the X Size parameter, specifies the size of the raster window that is read from the input image.

Y Size is the number of lines that define the window height.

If X Offset, Y Offset, X Size, and Y Size are not specified, the entire image is processed by default.

Transformation Type

Specifies the type of transformation to perform.

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

Transforming images into the frequency domain is useful for a variety of image processing operations (such as noise elimination and spatial filtering). FTF can be used to perform almost any type of filtering, provided that the user understands how each component of the Fourier (or other transformation) spectrum relates back to the original image.

For Fourier transformations (FIR or FMP), the input channel may contain either a complex-valued image, for example a single-look complex SAR image, or a real- or integer-valued image, such as a detected SAR image, or an optical satellite image. The output transform must be stored as 32-bit floating point values, either in a single complex channel, or in two real-valued channels. If a complex channel is used for output, the format is reset to FIR (real and imaginary values). For the COS, HAD and WAL transformations, one real- or integer-valued channel is required for input, and one 32-bit floating point channel is used for output.

For Fourier transformations, the zero frequency (DC component) is in the center of the transform image and progressively higher frequencies are plotted radially outward. For Cosine, Walsh, and Hadamard transformations, the zero frequency (DC component) is at the upper-left corner of the image.

Before running FTF, ensure that the specified output file (FILO) exists. If it does not, create it by executing CIM. For optimum performance, the transform file should be created in the tiled layout (for example, DBLAYOUT="TILED256" in CIM).

Because FTF does not require the entire image to be loaded into memory, there is no limit on the size of input image.

Interpretation

Interpretation of frequency transformed images can be quite complicated. This section provides some background for interpreting Fourier-transformed images. For more information, see the References section.

When the Fourier transformation is selected, the output domain is the two-dimensional frequency spectrum of the input image. If these results are output to the display, a fairly symmetric pattern will appear. Frequencies are along two directions (X and Y). The DC component (frequency = (0,0)) is at (N/2+1,M/2+1), where N and M denote image size in pixels and lines. On a 512 x 512 image, for example, the DC point should be at (257,257). Points away from the DC point indicate higher frequencies. The transformation at point (N/2+1+x,M/2+1+y) corresponds to the cosine wave component which repeats every N/x pixels along X direction and every M/y pixels along Y direction.

Filter application

A typical application of frequency transformation is to apply image filters in the frequency domain for image enhancement, restoration, and other purposes.

The basis for the filter technique is to eliminate or reduce some frequencies while keeping others. A filter can be specified in a graphics bitmap by masking image regions to eliminate. FFREQ allows such a graphical filter, as well as built-in high-pass/low-pass filters to be applied to the image. When the inverse transformation is performed on the filtered image, the result is the original image with some frequencies removed. For example, the result of keeping only high frequencies would be the enhancement of edges.

For a real-valued image (such as an image from an optical sensor, or a detected radar image), its Fourier transform exhibits a property of conjugate symmetry about the center of the image: at a pair of corresponding points, the real parts of the Fourier transformation are equal and the imaginary parts have the same magnitude but opposite signs. For complex-valued images (such as single-look complex radar images) there is no such symmetry.

The FFREQ module assumes that transforms stored in real-valued channels (DBIC) are produced from real-valued images, while transforms stored in complex-valued channels are created from complex images. Therefore, for the two Fourier transforms, the number and type of output channel(s) in the DBOC parameter should be selected according to the content of the input image. For a real input image, its FIR or FMP transform should be stored in two 32-bit floating point real channels. For a complex input image, its FIR transform should be stored in one 32-bit floating point complex channel.

Algorithm

References

Gonzalez, R.C. and Wintz, P. [1987]. Digital Image Processing. 2nd Edition, Addison-Wesley, Massachusetts.