[Paper Review] Fuzzy color model and clustering algorithm for color clustering problem

Dae‐Won Kim, Kwang H. Lee|arXiv (Cornell University)|Jul 9, 2024

Remote Sensing and Land Use6 citations

TL;DR

The paper proposes a three-dimensional fuzzy color ball model in CIELAB space to represent color uncertainty and a corresponding fuzzy clustering algorithm that uses this model for color data partitioning.

ABSTRACT

The research interest of this paper is focused on the efficient clustering task for an arbitrary color data. In order to tackle this problem, we have tried to model the inherent uncertainty and vagueness of color data using fuzzy color model. By taking fuzzy approach to color modeling, we could make a soft decision for the vague regions between neighboring colors. The proposed fuzzy color model defined a three dimensional fuzzy color ball and color membership computation method with two inter-color distances. With the fuzzy color model, we developed a new fuzzy clustering algorithm for an efficient partition of color data. Each fuzzy cluster set has a cluster prototype which is represented by fuzzy color centroid.

Motivation & Objective

• Motivate color clustering under uncertainty and vagueness in color data.
• Introduce a three-dimensional fuzzy color ball representation with JND-based volume.
• Define distance measures between color elements and between fuzzy colors.
• Develop a fuzzy clustering algorithm that uses fuzzy color centroids for partitioning color data.
• Provide an initialization scheme leveraging reference fuzzy colors to improve clustering outcomes.

Proposed method

• Define a three-dimensional fuzzy color ball with a center and a JND-based radius in CIELAB space.
• Introduce two distance measures: 1) element-element distance in CIELAB, 2) distance between a fuzzy color and a color element that accounts for center and JND.
• Define a membership function for fuzzy colors ensuring the sum of memberships for a color element equals 1.
• Formulate a fuzzy clustering objective J(F) that minimizes the weighted distance to fuzzy color centroids.
• Propose an initialization method using reference fuzzy colors from the Munsell wheel and CIELAB white/black/gray to seed centroids.
• Represent each fuzzy cluster centroid as a fuzzy color ball, enabling soft cluster assignment.

Experimental results

Research questions

• RQ1 How can color uncertainty and perceptual vagueness be modeled in a color clustering framework?
• RQ2 Can a fuzzy color ball representation combined with specialized distance measures improve color data clustering compared to crisp approaches?
• RQ3 How should fuzzy memberships to color clusters be computed and constrained (sum to 1) in this context?
• RQ4 What initialization strategy yields better convergence for fuzzy color-based clustering?
• RQ5 What is the impact of using JND-based volumes on color similarity judgments in clustering?

Key findings

• A fuzzy color model based on a 3D fuzzy ball in CIELAB space represents color centers and perceptual tolerance via JND radii.
• Two distance measures are defined: ρ between color elements and δ between a fuzzy color and a color element, incorporating center distance and JND.
• A membership function μ for fuzzy colors is defined so that memberships sum to 1 for any color element and reflect proximity to fuzzy color centers.
• A fuzzy clustering objective J(F) is minimized to partition color data into fuzzy clusters with centroids represented by fuzzy colors.
• An initialization scheme uses 13 reference fuzzy colors from the Munsell wheel and CIELAB axes to seed cluster centers, improving initialization.
• The approach enables soft decisions in color clustering and provides a uniform, perceptually grounded color space for clustering.