Efficiently Computing Piecewise Flat Embeddings for Data Clustering and Image Segmentation
This incremental improvement makes PFE more practical for large-scale image segmentation and data clustering applications.
The paper tackles the computational inefficiency of piecewise flat embeddings (PFE) for image segmentation by proposing parallelization and an iterative linear solver, achieving an order of magnitude speedup without performance loss on a public image database.
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.