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

Learning image components for object recognition

In order to perform object recognition it is necessary to learn representations of the underlying components of images. Such components correspond to objects, object-parts, or features. Non-negative matrix factorisation is a generative model that has been specifically proposed for finding such meaningful representations of image data, through the use of non-negativity constraints on the factors. This article reports on an empirical investigation of the performance of non-negative matrix factorisation algorithms. It is found that such algorithms need to impose additional constraints on the sparseness of the factors in order to successfully deal with occlusion. However, these constraints can themselves result in these algorithms failing to identify image components under certain conditions. In contrast, a recognition model (a competitive learning neural network algorithm) reliably and accurately learns representations of elementary image features without such constraints

Constructing Hierarchical Image-tags Bimodal Representations for Word Tags Alternative Choice

This paper describes our solution to the multi-modal learning challenge of ICML. This solution comprises constructing three-level representations in three consecutive stages and choosing correct tag words with a data-specific strategy. Firstly, we use typical methods to obtain level-1 representations. Each image is represented using MPEG-7 and gist descriptors with additional features released by the contest organizers. And the corresponding word tags are represented by bag-of-words model with a dictionary of 4000 words. Secondly, we learn the level-2 representations using two stacked RBMs for each modality. Thirdly, we propose a bimodal auto-encoder to learn the similarities/dissimilarities between the pairwise image-tags as level-3 representations. Finally, during the test phase, based on one observation of the dataset, we come up with a data-specific strategy to choose the correct tag words leading to a leap of an improved overall performance. Our final average accuracy on the private test set is 100%, which ranks the first place in this challenge.Comment: 6 pages, 1 figure, Presented at the Workshop on Representation Learning, ICML 201

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