A Novel Algorithm for Exact Concave Hull Extraction

TL;DR

This paper introduces a new algorithm for extracting exact, vertex-minimized concave hulls with high resolution, improving accuracy and efficiency for applications like image compression and data analysis.

Contribution

The novel algorithm achieves pixel-perfect concave hull extraction with tunable speed-efficiency, outperforming approximate methods in accuracy and applicability.

Findings

Significant improvements in image compression quality.

Effective application across biomedical and natural images.

Enhanced downstream data retrieval and visualization.

Abstract

Region extraction is necessary in a wide range of applications, from object detection in autonomous driving to analysis of subcellular morphology in cell biology. There exist two main approaches: convex hull extraction, for which exact and efficient algorithms exist and concave hulls, which are better at capturing real-world shapes but do not have a single solution. Especially in the context of a uniform grid, concave hull algorithms are largely approximate, sacrificing region integrity for spatial and temporal efficiency. In this study, we present a novel algorithm that can provide vertex-minimized concave hulls with maximal (i.e. pixel-perfect) resolution and is tunable for speed-efficiency tradeoffs. Our method provides advantages in multiple downstream applications including data compression, retrieval, visualization, and analysis. To demonstrate the practical utility of our approach, we focus on image compression. We demonstrate significant improvements through context-dependent compression on disparate regions within a single image (entropy encoding for noisy and predictive encoding for the structured regions). We show that these improvements range from biomedical images to natural images. Beyond image compression, our algorithm can be applied more broadly to aid in a wide range of practical applications for data retrieval, visualization, and analysis.