# American Institute of Mathematical Sciences

## Segmentation of color images using mean curvature flow and parametric curves

 1 Czech Technical University in Prague, Trojanova 13,120 00 Prague, Czech Republic 2 Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan

* Corresponding author: Petr Pauš

Received  January 2019 Revised  February 2020 Published  June 2020

Automatic detection of objects in photos and images is beneficial in various scientific and industrial fields. This contribution suggests an algorithm for segmentation of color images by the means of the parametric mean curvature flow equation and CIE94 color distance function. The parametric approach is enriched by the enhanced algorithm for topological changes where the intersection of curves is computed instead of unreliable curve distance. The result is a set of parametric curves enclosing the object. The algorithm is presented on a test image and also on real photos.

Citation: Petr Pauš, Shigetoshi Yazaki. Segmentation of color images using mean curvature flow and parametric curves. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020389
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##### References:
Algorithm for topological changes of a closed curve $\Gamma$ which overlaps itself under the external force. The intersections are computed and the overlapping segments of the curve are removed. The resulting two closed curves continue evolution in time
Original image with white background (left), gray-scale intensity image from a red color (middle), and simple conversion to gray-scale and inversion (right)
Artificial color image segmentation with the red reference color
Comparison of the color distance segmentation (left) and simple gray-scale conversion segmentation (right)
Original yellow flower photo (left), the distance image from a yellow color (middle), and a simple conversion to gray-scale (right)
Comparison of the color distance segmentation (left) and simple gray-scale conversion segmentation (right) for a yellow flower
The photo of a cloud and its distance image from the almost white (very light light blue) color
Segmentation of the original cloud image
Segmentation of the sunflower with different shades of yellow
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