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

Hyperspectral image representation through alpha-trees

International audienceα-trees provide a hierarchical representation of an image into partitions of regions with increasing heterogeneity. This model, inspired from the single-linkage paradigm, has recently been revisited for grayscale images and has been successfully used in the field of remote sensing. This article shows how this representation can be adapted to more complex data here hyperspectral images, according to different strategies. We know that the measure of distance between two neighbouring pixels is a key element for the quality of the underlying tree, but usual metrics are not satisfying. We show here that a relevant solution to understand hyperspectral data relies on the prior learning of the metric to be used and the exploitation of domain knowledge

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

Constructive links between some morphological hierarchies on edge-weighted graphs

International audienceIn edge-weighted graphs, we provide a unified presentation of a family of popular morphological hierarchies such as component trees, quasi flat zones, binary partition trees, and hierarchical watersheds. For any hierarchy of this family, we show if (and how) it can be obtained from any other element of the family. In this sense, the main contribution of this paper is the study of all constructive links between these hierarchies

Efficient Schemes for Computing α-tree Representations

International audienceHierarchical image representations have been addressed by various models by the past, the max-tree being probably its best representative within the scope of Mathematical Morphology. However, the max-tree model requires to impose an ordering relation between pixels, from the lowest values (root) to the highest (leaves). Recently, the α-tree model has been introduced to avoid such an ordering. Indeed, it relies on image quasi-flat zones, and as such focuses on local dissimilarities. It has led to successful attempts in remote sensing and video segmentation. In this paper, we deal with the problem of α-tree computation, and propose several efficient schemes which help to ensure real-time (or near-real time) morphological image processing

Fast image and video segmentation based on alpha-tree multiscale representation

International audienceIn this paper, we propose to rely on a recent image representation model, namely the α-tree, to achieve efficient segmentation of images and videos. The α-tree is a multiscale representation of an image, based on its quasi-flat zones. An in-depth study of this tree reveals some interesting features of image pixels and regions. These features are then used in the design of both automatic and interactive segmentation algorithms. Interactivity is achieved thanks to a new and efficient implementation scheme. Experiments on the Berkeley Segmentation Dataset lead to very promising results

Nanopatterning Gold by Templated Solid State Dewetting on the Silica Warp and Weft of Diatoms

The diatom, Nitzschia palea, exhibits complex silica shell (frustule) topography that resembles the warp and weft pattern of woven glass. The surface is perforated with a rhombic lattice of roughly oblong pores between periodically undulating transverse weft costae. Exfoliated frustules can be used to template gold nanoparticles by thermally induced dewetting of thin gold films. Acting as templates for the process, the frustules give rise to two coexisting hierarchies of particle sizes and patterned distributions of nanoparticles. By examining temperature dependent dewetting of 5, 10, and 15 nm Au films for various annealing times, we establish conditions for particle formation and patterning. The 5 nm film gives distributions of small particles randomly distributed over the surface and multiple particles at the rhombic lattice points in the pores. Thicker films yield larger faceted particles on the surface and particles that exhibit shapes that are roughly conformal with the shape of the pore container. The pores and costae are sources of curvature instabilities in the film that lead to mass transport of gold and selective accumulation in the weft valleys and pores. We suggest that, with respect to dewetting, the frustule comprises 2-dimensional sublattices of trapping sites. The pattern of dewetting is radically altered by interposing a self-assembled molecular adhesive of mercaptopropyltrimethoxysilane between the Au film overlayer and the frustule. By adjusting the interfacial energy in this manner, a fractal-like overlay of Au islands coexists with a periodic distribution of nanoparticles in the pores

Connected image processing with multivariate attributes: an unsupervised Markovian classification approach

International audienceThis article presents a new approach for constructing connected operators for image processing and analysis. It relies on a hierarchical Markovian unsupervised algorithm in order to classify the nodes of the traditional Max-Tree. This approach enables to naturally handle multivariate attributes in a robust non-local way. The technique is demonstrated on several image analysis tasks: filtering, segmentation, and source detection, on astronomical and biomedical images. The obtained results show that the method is competitive despite its general formulation. This article provides also a new insight in the field of hierarchical Markovian image processing showing that morphological trees can advantageously replace traditional quadtrees

Physical Combinatorics and Quasiparticles

We consider the physical combinatorics of critical lattice models and their associated conformal field theories arising in the continuum scaling limit. As examples, we consider A-type unitary minimal models and the level-1 sl(2) Wess-Zumino-Witten (WZW) model. The Hamiltonian of the WZW model is the $U_q(sl(2))$ invariant XXX spin chain. For simplicity, we consider these theories only in their vacuum sectors on the strip. Combinatorially, fermionic particles are introduced as certain features of RSOS paths. They are composites of dual-particles and exhibit the properties of quasiparticles. The particles and dual-particles are identified, through an energy preserving bijection, with patterns of zeros of the eigenvalues of the fused transfer matrices in their analyticity strips. The associated (m,n) systems arise as geometric packing constraints on the particles. The analyticity encoded in the patterns of zeros is the key to the analytic calculation of the excitation energies through the Thermodynamic Bethe Ansatz (TBA). As a by-product of our study, in the case of the WZW or XXX model, we find a relation between the location of the Bethe root strings and the location of the transfer matrix 2-strings.Comment: 57 pages, in version 2: typos corrected, some sentences clarified, one appendix remove