# Documentation

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# Image Transforms

Perform Fourier, Discrete Cosine, Radon, and Fan-beam transforms

## Functions

 `bwdist` Distance transform of binary image `bwdistgeodesic` Geodesic distance transform of binary image `graydist` Gray-weighted distance transform of grayscale image `hough` Hough transform `dct2` 2-D discrete cosine transform `dctmtx` Discrete cosine transform matrix `fan2para` Convert fan-beam projections to parallel-beam `fanbeam` Fan-beam transform `idct2` 2-D inverse discrete cosine transform `ifanbeam` Inverse fan-beam transform `iradon` Inverse Radon transform `para2fan` Convert parallel-beam projections to fan-beam `radon` Radon transform `fft2` 2-D fast Fourier transform `fftshift` Shift zero-frequency component to center of spectrum `ifft2` 2-D inverse fast Fourier transform `ifftshift` Inverse FFT shift

## Examples and How To

Detect Lines Using the Radon Transform

This example shows how to use the Radon transform to detect lines in an image.

Reconstructing an Image from Parallel Projection Data

The commands below illustrate how to reconstruct an image from parallel projection data.

Reconstruct Image using Inverse Fanbeam Projection

This example shows how to use `fanbeam` and `ifanbeam` to form projections from a sample image and then reconstruct the image from the projections.

## Concepts

Fourier Transform

Defines the Fourier transform and some of its applications in image processing

Discrete Cosine Transform

Describes the discrete cosine transform (DCT) of an image and its application, particularly in image compression

Radon Transform

Describes how the `radon` function computes projections of an image matrix along specified directions

The Inverse Radon Transformation

Describes how the `iradon` function reconstructs images from projection data

Inverse Radon Transform Definition

The `iradon` function inverts the Radon transform and can therefore be used to reconstruct images.

Fan-Beam Projection Data

Describes how the `fanbeam` function computes projections of an image matrix along paths that radiate from a specific source

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