Image segmentation by combining the strengths of Relative Fuzzy Connectedness and Graph Cut

Abstract

We introduce an image segmentation algorithm GC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sup> , which combines, in a novel manner, the strengths of two popular algorithms: Relative Fuzzy Connectedness (RFC) and (standard) Graph Cut (GC). We show, both theoretically and experimentally, that GC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sup> preserves robustness of RFC with respect to the seed choice (thus, avoiding “shrinking problem” of GC), while keeping GC's bigger control over “leaking though the weak boundary.” The theoretical analysis of GC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sup> is greatly facilitated by our recent theoretical results that RFC belongs to the Generalized GC (GGC) segmentation algorithms framework. In our implementation of GC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sup> we use, as a subroutine, a version of RFC algorithm (based on Image Foresting Transform) that runs (provably) in linear time with respect to the image size. This results in GC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sup> running in a time close to linear.