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

TL;DR

This paper introduces a novel method that transforms colon tissue architecture into sinusoid waves using LCPC transform and applies FFT to quantify spatial complexity, aiding in polyp classification.

Contribution

It presents the LCPC transform combined with FFT as a new technique to quantify and categorize the spatial complexity of colon polyps.

Findings

The method successfully differentiates histological grades based on frequency signatures.

It provides a quantitative index of tissue complexity.

The approach enhances polyp classification accuracy.

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].