Braids Of Partitions


In obtaining a tractable solution to the problem of extractinga minimal partition from hierarchy or tree by dynamic programming, we introduce the braids of partition and h-increasing energies, the former extending the solution space from a hierarchy to a larger set, the latter describing the family of energies, for which one can obtain the solution by a dynamic programming. We also provide the singularity condition for the existence of unique solution, leading to the definition of the energetic lattice. The paper also identifies various possible braids in literature and how this structure relaxes the segmentation problem.[Read More]






Optimal cut problem


Hierarchical segmentation is a multi-scale analysis of an image and provides a series of simplifying nested partitions. Such a hierarchy is rarely an end by itself and requires external criteria or heuristics to solve problems of image segmentation, texture extraction and semantic image labelling. In this theoretical paper we first propose a novel energy minimization framework to formulate optimization problems on hierarchies of segmentations. Second we provide the three important notions of h-increasing, singular, and scale increasing energies, necessary to solve the global combinatorial ptimization problem of partition selection and which results in linear time dynamic programs. Common families of such energies are summarized, and also a method to generate new ones is described. Finally we demonstrate the application of this framework on problems of image segmentation and texture enhancement. [Read More]





Reordering contours by saliency transform and Ground truth energies


During the evaluation of ground truth segmentation one problem is the evauation of a numerical measure that determines if the given image segmentation is close to the expert/human drawn ground truth. Given a hierarchy of segmentations one faces the problem of chosing which partition amongst all cuts is closest to a given ground truth. We evaluate a localized haussdorf distance locally for every super-pixel segment belonging to the input hierarchy of segmentations corresponding to the input image, using the ground truth partition contours and their distance functions. [Read More]






Hyperspectral image processing for Tumor detection


Hyperspectral images of high spatial and spectral resolutions are employed to perform the challenging task of brain tissue characterization and subsequent segmentation for visualization of in-vivo images. Each pixel is a high-dimensional spectrum. Working on the hypothesis of pure-pixels on account of high spectral resolution, we perform unsupervised clustering by hierarchical non-negative matrix factorization to identify the pure- pixel spectral signatures of blood, brain tissues, tumor and other materials. This subspace clustering was further used to train a random forest for subsequent classification of test set images constituent of in-vivo and ex-vivo images. Unsupervised hierarchical clustering helps visualize tissue structure in in-vivo test images and provides a inter-operative tool for surgeons. Furthermore the study also provides a preliminary study of the classification and sources of errors in the classification process.
[Read More][EU project webpage]




Fun: Morphological Flooding of Oceans - A thought experiment from "Whatif xkcd".

Fun: Solving mazes using morphological reconstruction filtering Example in openCV .