Efficiently Computing Piecewise Flat Embeddings for Data Clustering and Image Segmentation

TL;DR

This paper enhances the computational efficiency of piecewise flat embeddings (PFE) for image segmentation by reformulating algorithms for parallel processing and employing iterative linear solvers, enabling practical large-scale data clustering.

Contribution

It introduces two key improvements to PFE computation: parallelizable reformulation and an iterative solver, significantly speeding up processing without losing segmentation quality.

Findings

PFE speed increased by an order of magnitude.

Segmentation performance remains high after optimization.

Applicable to large datasets beyond image segmentation.

Abstract

Image segmentation is a popular area of research in computer vision that has many applications in automated image processing. A recent technique called piecewise flat embeddings (PFE) has been proposed for use in image segmentation; PFE transforms image pixel data into a lower dimensional representation where similar pixels are pulled close together and dissimilar pixels are pushed apart. This technique has shown promising results, but its original formulation is not computationally feasible for large images. We propose two improvements to the algorithm for computing PFE: first, we reformulate portions of the algorithm to enable various linear algebra operations to be performed in parallel; second, we propose utilizing an iterative linear solver (preconditioned conjugate gradient) to quickly solve a linear least-squares problem that occurs in the inner loop of a nested iteration. With these two computational improvements, we show on a publicly available image database that PFE can be sped up by an order of magnitude without sacrificing segmentation performance. Our results make this technique more practical for use on large data sets, not only for image segmentation, but for general data clustering problems.