On the equivalence between hierarchical segmentations and ultrametric watersheds

We study hierarchical segmentation in the framework of edge-weighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical segmentations. We end this paper by showing how to use the proposed framework in practice in the example of constrained connectivity; in particular it allows to compute such a hierarchy following a classical watershed-based morphological scheme, which provides an efficient algorithm to compute the whole hierarchy.Comment: 19 pages, double-colum

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

New characterizations of minimum spanning trees and of saliency maps based on quasi-flat zones

We study three representations of hierarchies of partitions: dendrograms (direct representations), saliency maps, and minimum spanning trees. We provide a new bijection between saliency maps and hierarchies based on quasi-flat zones as used in image processing and characterize saliency maps and minimum spanning trees as solutions to constrained minimization problems where the constraint is quasi-flat zones preservation. In practice, these results form a toolkit for new hierarchical methods where one can choose the most convenient representation. They also invite us to process non-image data with morphological hierarchies

Learning image segmentation and hierarchies by learning ultrametric distances

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 100-105).In this thesis I present new contributions to the fields of neuroscience and computer science. The neuroscientific contribution is a new technique for automatically reconstructing complete neural networks from densely stained 3d electron micrographs of brain tissue. The computer science contribution is a new machine learning method for image segmentation and the development of a new theory for supervised hierarchy learning based on ultrametric distance functions. It is well-known that the connectivity of neural networks in the brain can have a dramatic influence on their computational function . However, our understanding of the complete connectivity of neural circuits has been quite impoverished due to our inability to image all the connections between all the neurons in biological network. Connectomics is an emerging field in neuroscience that aims to revolutionize our understanding of the function of neural circuits by imaging and reconstructing entire neural circuits. In this thesis, I present an automated method for reconstructing neural circuitry from 3d electron micrographs of brain tissue. The cortical column, a basic unit of cortical microcircuitry, will produce a single 3d electron micrograph measuring many 100s terabytes once imaged and contain neurites from well over 100,000 different neurons. It is estimated that tracing the neurites in such a volume by hand would take several thousand human years. Automated circuit tracing methods are thus crucial to the success of connectomics. In computer vision, the circuit reconstruction problem of tracing neurites is known as image segmentation. Segmentation is a grouping problem where image pixels belonging to the same neurite are clustered together. While many algorithms for image segmentation exist, few have parameters that can be optimized using groundtruth data to extract maximum performance on a specialized dataset. In this thesis, I present the first machine learning method to directly minimize an image segmentation error. It is based the theory of ultrametric distances and hierarchical clustering. Image segmentation is posed as the problem of learning and classifying ultrametric distances between image pixels. Ultrametric distances on point set have the special property that(cont.) they correspond exactly to hierarchical clustering of the set. This special property implies hierarchical clustering can be learned by directly learning ultrametric distances. In this thesis, I develop convolutional networks as a machine learning architecture for image processing. I use this powerful pattern recognition architecture with many tens of thousands of free parameters for predicting affinity graphs and detecting object boundaries in images. When trained using ultrametric learning, the convolutional network based algorithm yields an extremely efficient linear-time segmentation algorithm. In this thesis, I develop methods for assessing the quality of image segmentations produced by manual human efforts or by automated computer algorithms. These methods are crucial for comparing the performance of different segmentation methods and is used through out the thesis to demonstrate the quality of the reconstructions generated by the methods in this thesis.by Srinivas C. Turaga.Ph.D

Hierarchical Image Representation Simplification Driven by Region Complexity

International audienceThis article presents a technique that arranges the elements of hierarchical representations of images according to a coarseness attribute. The choice of the attribute can be made according to prior knowledge about the content of the images and the intended application. The transformation is similar to filtering a hierarchy with a non-increasing attribute, and comprises the results of multiple simple filterings with an increasing attribute. The transformed hierarchy can be used for search space reduction prior to the image analysis process because it allows for direct access to the hierarchy elements at the same scale or a narrow range of scales

Machine Learning for Instance Segmentation

Volumetric Electron Microscopy images can be used for connectomics, the study of brain connectivity at the cellular level. A prerequisite for this inquiry is the automatic identification of neural cells, which requires machine learning algorithms and in particular efficient image segmentation algorithms. In this thesis, we develop new algorithms for this task. In the first part we provide, for the first time in this field, a method for training a neural network to predict optimal input data for a watershed algorithm. We demonstrate its superior performance compared to other segmentation methods of its category. In the second part, we develop an efficient watershed-based algorithm for weighted graph partitioning, the \emph{Mutex Watershed}, which uses negative edge-weights for the first time. We show that it is intimately related to the multicut and has a cutting edge performance on a connectomics challenge. Our algorithm is currently used by the leaders of two connectomics challenges. Finally, motivated by inpainting neural networks, we create a method to learn the graph weights without any supervision