Santiago Velasco-Forero

Local Mutual Information for Dissimilarity-Based Image Segmentation

Connective segmentation based on the definition of a dissimilarity measure on pairs of adjacent pixels is an appealing framework to develop new hierarchical segmentation methods. Usually, the dissimilarity is fully determined by the intensity values of the considered pair of adjacent pixels, so that it is independent of the values of the other image pixels. In this paper, we explore dissimilarity measures depending on the overall image content encapsulated in its local mutual information and show its invariance to information preserving transforms. This is investigated in the framework of the connective segmentation and constrained connectivity paradigms and leads to the concept of dependent connectivities. An efficient probability estimator based on depth functions is proposed to handle multi-dimensional images. Experiments conducted on hyper-spectral and multi-angular remote sensing images highlight the robustness of the proposed approach.

SHREC'13 track: retrieval on textured 3D models

This contribution reports the results of the SHREC 2013 track: Retrieval on Textured 3D Models, whose goal is to evaluate the performance of retrieval algorithms when models vary either by geometric shape or texture, or both. The collection to search in is made of 240 textured mesh models, divided into 10 classes. Each model has been used in turn as a query against the remaining part of the database. For a given query, the goal was to retrieve the most similar objects. The track saw six participants and the submission of eleven runs.

On Nonlocal Mathematical Morphology

In this paper, nonlocal mathematical morphology operators are introduced as a natural extension of nonlocal-means in the max-plus algebra. Firstly, we show that nonlocal morphology is a particular case of adaptive morphology. Secondly, we present the necessary properties to have algebraic properties on the associated pair of transformations. Finally, we recommend a sparse version to introduce an efficient algorithm that computes these operators in reasonable computational time.

Stochastic Morphological Filtering and Bellman-Maslov Chains

This paper introduces a probabilistic framework for adaptive morphological dilation and erosion. More precisely our probabilistic formalization is based on using random walk simulations for a stochastic estimation of adaptive and robust morphological operators. Hence, we propose a theoretically sound morphological counterpart of Monte Carlo stochastic filtering. The approach by simulations is inefficient but particularly tailorable for introducing different kinds of adaptability. From a theoretical viewpoint, stochastic morphological operators fit into the framework of Bellman-Maslov chains, the ( max , + )-counterpart of Markov chains, which the basis behind the efficient implementations using sparse matrix products.

Vector Ordering and Multispectral Morphological Image Processing

This chapter illustrates the suitability of recent multivariate ordering approaches to morphological analysis of colour and multispectral images working on their vector representation. On the one hand, supervised ordering renders machine learning notions and image processing techniques, through a learning stage to provide a total ordering in the colour/multispectral vector space. On the other hand, anomaly-based ordering, automatically detects spectral diversity over a majority background, allowing an adaptive processing of salient parts of a colour/multispectral image. These two multivariate ordering paradigms allow the definition of morphological operators for multivariate images, from algebraic dilation and erosion to more advanced techniques as morphological simplification, decomposition and segmentation. A number of applications are reviewed and implementation issues are discussed in detail.

Conditional Toggle Mappings: Principles and Applications

We study a class of mathematical morphology filters to operate conditionally according to a set of pixels marked by a binary mask. The main contribution of this paper is to provide a general framework for several applications including edge enhancement and image denoising, when it is affected by salt-and-pepper noise. We achieve this goal by revisiting shock filters based on erosions and dilations and extending their definition to take into account the prior definition of a mask of pixels that should not be altered. New definitions for conditional erosions and dilations leading to the concept of conditional toggle mapping. We also investigate algebraic properties as well as the convergence of the associate shock filter. Experiments show how the selection of appropriate methods to generate the masks lead to either edge enhancement or salt-and-pepper denoising. A quantitative evaluation of the results demonstrates the effectiveness of the proposed methods. Additionally, we analyse the application of conditional toggle mapping in remote sensing as pre-filtering for hierarchical segmentation.

Mathematical Morphology for Real-Valued Images on Riemannian Manifolds

This paper introduces mathematical morphology for real-valued images whose support space is a Riemannian manifold. The starting point consists in replacing the Euclidean distance in the canonic quadratic structuring function by the Riemannian distance. Besides the definition of Riemannian dilation/erosion and Riemannian opening/closing, their properties are explored. We generalize also some theoretical results on Lasry–Lions regularization for Cartan–Hadamard manifolds. Theoretical connections with previous works on adaptive morphology and on manifold shape are considered. Various useful image manifolds are formalized, with an example using real-valued 3D surfaces.

Complete Lattice Structure of Poincaré Upper-Half Plane and Mathematical Morphology for Hyperbolic-Valued Images

Mathematical morphology is a nonlinear image processing methodology based on the application of complete lattice theory to spatial structures. Let us consider an image model where at each pixel is given a univariate Gaussian distribution. This model is interesting to represent for each pixel the measured mean intensity as well as the variance (or uncertainty) for such measurement. The aim of this paper is to formulate morphological operators for these images by embedding Gaussian distribution pixel values on the Poincare upper-half plane. More precisely, it is explored how to endow this classical hyperbolic space with partial orderings which lead to a complete lattice structure.

Supervised Morphology for Structure Tensor-Valued Images Based on Symmetric Divergence Kernels

Mathematical morphology is a nonlinear image processing methodology based on computing min/max operators in local neighbourhoods. In the case of tensor-valued images, the space of SPD matrices should be endowed with a partial ordering and a complete lattice structure. Structure tensor describes robustly the local orientation and anisotropy of image features. Formulation of mathematical morphology operators dealing with structure tensor images is relevant for texture filtering and segmentation. This paper introduces tensor-valued mathematical morphology based on a supervised partial ordering, where the ordering mapping is formulated by means of positive definite kernels and solved by machine learning algorithms. More precisely, we focus on symmetric divergences for SPD matrices and associated kernels.

Multivariate diffusion tensor and induced segmentation

This paper explore the problem of unsupervised hierarchical segmentation for hyperspectral images using a multivariate version of the structure tensor [1] and morphological segmentation methods based on a pixel dissimilarity measures [2]. This spatial structure tensor fusions the edge information along the spectral dimension of the gradient by using weights based on the heat kernel. The unsupervised morphological segmentation uses a graph-based model where the pixels are the nodes. A dissimilarity function based on the eccentricity of the local structure tensor at each node is proposed to define the weights of the edges. With a global threshold, α, applied to the distances between nodes an α-connectivity is defined. As α increases its value, it can be proved that a hierarchy, i.e an ordered sequence of α-connected components is formed, producing a hierarchy of connective segmentations. Segmentation maps using the proposed tensor-based dissimilarity function, the Euclidean distance and the Spectral Angle Distance were performed and tested with the Endmember Extraction Problem. The comparison of the endmembers produced using the proposed segmentation with each of the above measures and the endmembers from the original image shows that the endmembers produced using the tensor-based dissimilarity function have the smallest averaged SAD than using the other measures.