Homological spanning forest framework for 2D image analysis

Homological Tree-Based Strategies for Image Analysis

Homological characteristics of digital objects can be obtained in a straightforward manner computing an algebraic map φ over a finite cell complex K (with coefficients in the finite field F2 = {0, 1}) which represents the digital object [9]. Computable homological information includes the Euler characteristic, homology generators and representative cycles, higher (co)homology operations, etc. T...

2D image segmentation using minimum spanning trees

Homological Computation Using Spanning Trees

We introduce here a new F2 homology computation algorithm based on a generalization of the spanning tree technique on a finite 3-dimensional cell complex K embedded in R. We demonstrate that the complexity of this algorithm is linear in the number of cells. In fact, this process computes an algebraic map φ over K, called homology gradient vector field (HGVF), from which it is possible to infer ...

The 2D-directed spanning forest is almost surely a tree

We consider the Directed Spanning Forest (DSF) constructed as follows: given a Poisson point process N on the plane, the ancestor of each point is the nearest vertex of N having a strictly larger abscissa. We prove that the DSF is actually a tree. Contrary to other directed forests of the literature, no Markovian process can be introduced to study the paths in our DSF. Our proof is based on a c...

An Iterative Spanning Forest Framework for Superpixel Segmentation

Superpixel segmentation has become an important research problem in image processing. In this paper, we propose an Iterative Spanning Forest (ISF) framework, based on sequences of Image Foresting Transforms, where one can choose i) a seed sampling strategy, ii) a connectivity function, iii) an adjacency relation, and iv) a seed pixel recomputation procedure to generate improved sets of connecte...