Forward and backward mapping of image to 2D vector field using fiber bundle color space

TL;DR

This paper introduces a fiber bundle color space model for mapping images to 2D vector fields and vice versa, enabling advanced vector analysis of color images based on psychophysical color perception.

Contribution

It proposes a novel fiber bundle color space and a homomorphic mapping framework for converting between color images and vector fields, incorporating psychophysical color perception rules.

Findings

Demonstrated a forward mapping from images to vector fields.

Developed a backward mapping algorithm for reconstructing images from vector fields.

Applied the method to visualize magnetic vector fields as color images.

Abstract

We introduce the concept of a fiber bundle color space, which acts according to the psychophysiological rules of trichromacy perception of colors by a human. The image resides in the fiber bundle base space and the fiber color space contains color vectors. Further we propose the decomposition of color vectors into spectral and achromatic parts. A homomorphism of a color image and constructed two-dimensional vector field is demonstrated that allows us to apply well-known advanced methods of vector analysis to a color image, i.e. ultimately give new numerical characteristics of the image. Appropriate image to vector field forward mapping is constructed. The proposed backward mapping algorithm converts a two-dimensional vector field to color image. The type of image filter is described using sequential forward and backward mapping algorithms. An example of the color image formation on the base of two-dimensional magnetic vector field scattered by a typical pipe line defect is given.