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Radon

Radon[image]
gives an image representing the discrete Radon transform of image.
Radon
specifies the width w and the height h of the resulting image.
Radon
computes the Radon transform only for angles from to .
  • Radon[image] computes the Radon transform of image and returns the result as an image in which each pixel value gives a measure for the presence of a line in image.
  • By default, Radon uses a normal line parametrization , where and are image coordinates, is the distance between the origin of the image coordinate system and the line, and is the angle between the normal and the horizontal axis.
  • Angles are given in radians. An angle in the image corresponds to a vertical line.
  • In the image returned by Radon[image], the columns represent angles in the range to , and the rows represent pixel distances in the range to , where is the length of the diagonal of image.
  • The height of the image returned by Radon[image] is equal to the length of the diagonal of image. The width is chosen so that the image and its Radon transform have approximately the same resolution.
  • Radon returns an image in which values are normalized so that the highest possible value is 1.
  • Radon computes the Radon transform for angles in the range to .
  • Radon uses as the origin of the image coordinate system. By default, is set to be the center of the image.
  • The origin is specified in the standard image coordinate system where runs from to width and runs from to height. Position corresponds to the bottom-left corner of the image.
  • Radon uses a line parametrization with as the origin of normal vectors and distances running in the range from to .
  • Radon works with binary, grayscale, and other images.
  • Radon operates separately on each channel in an image.
  • Radon[image, ..., Method->method] specifies the method to use to compute the Radon transform.
  • With the default setting Method, Radon computes for each pixel of the resulting image the sum of the pixels along the corresponding line in the input image, divided by the number of pixels on the diagonal. Radon uses bilinear subpixel interpolation.     
  • With Method, the standard Hough transform is computed. For each pixel in the input image, a value is accumulated in each column of the resulting image. The Hough transform iterates over the pixels in the input image, accumulating the intensity value at the corresponding point in each column of the output image.
Radon transform of a CT image of a head:
Radon transform of a grayscale image:
Radon transform of a color image:
Compute the standard Hough transform:
Radon transform of a CT image of a head:
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Radon transform of a grayscale image:
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Radon transform of a color image:
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Compute the standard Hough transform:
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The Radon transform of an image with rectangular objects:
The Radon transform of the perimeters of rectangles shows pairs of peaks:
Standard Hough transform is typically fast, but it also includes some artifacts:
Radon transform gives a more accurate result:
Radon transform of a color image:
Use Chan-Vese segmentation to locate the maxima:
Radon transform of a white disk:
Computing the Radon transform of a noisy image shows the sinusoidal parameter range of the transformed image:
Radon transform of an arbitrary line:
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