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arXiv · 1801.06752

Translating the Architectural Complexity of the Colon or Polyp into a Sinusoid Wave for Classification via the Fast Fourier Transform

David H. Nguyen
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Abstract

There is no method to quantify the spatial complexity within colon polyps. This paper describes a spatial transformation that translates the tissue architecture within a polyp, or a normal colon lining, into a complex sinusoid wave composed of discrete points. This sinusoid wave can then undergo the Fast Fourier Transform to obtain a spectrum of frequencies that represents the sinusoid wave. This spectrum can then serve as a signature of the spatial complexity [an index] within the polyp. By overlaying vertical lines that radiate from the bottom middle [like a fold-out fan] of an image of a polyp stained by hematoxylin and eosin, the image is segmented into sectors. Each vertical line also forms an angle with the horizontal axis of the image, ranging from 0 degrees to 180 degrees rising counter clockwise. Each vertical line will intersect with various features of the polyp [border of lumens, border of epithelial lining]. Each of these intersections is a point that can be characterized by its distance from the origin [this distance is also a magnitude of that point]. Thus, each intersection between radial line and polyp feature can be mapped by polar coordinates [radius length, angle measure]. By summing the distance of all points along the same radial line, each radial line that divides the image becomes one value. Plotting these values [y variable] against the angle of each radial line from the horizontal axis [x variable] results in a sinusoid wave consisting of discrete points. This method is referred to as the Linearized Compressed Polar Coordinates [LCPC] Transform. The LCPC transform, in conjunction with the Fast Fourier Transform, can reduce the complexity of visually hidden histological grades in colon polyps into categories of similar wave frequencies [each histological grade has a signature consisting of a handful of frequencies].

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David H. Nguyen. 2018-01-21. Translating the Architectural Complexity of the Colon or Polyp into a Sinusoid Wave for Classification via the Fast Fourier Transform. https://arxiv.org/abs/1801.06752

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