MORPHOLOGICAL SPATIAL PATTERN ANALYSIS: OPEN SOURCE RELEASE

Abstract. The morphological segmentation of binary patterns provides an effective method for characterising spatial patterns with emphasis on connections between their parts as measured at varying analysis scales. The method is widely used for the analysis of landscape patterns such as those related to the fragmentation of forests or other natural land cover classes. This can be explained by its effectiveness at capturing the complexity of binary patterns and their connections by partitioning the foreground pixels of the corresponding binary images into mutually exclusive classes. While the principles of the method are conceptually simple, the definition of the classes relies on a series of advanced mathematical morphology operations whose actual implementation is not straightforward. In this paper, we propose an open source code for MSPA and detail its main components in the form of pseudo-code. We demonstrate its effectiveness for asynchronous processing of tera-pixel images and the synchronous exploratory analysis and rendering with Jupyter notebooks

Microfossils and depositional environment of late Dinantian carbonates at Heibaart (Northern Belgium)

The core intervals of five boreholes in the Dinantian carbonates of the Heibaart area in northern Belgium have been investigated on their microfossil contents and lithofacies. The foraminifers suggest an early Warnantian age. No conodonts have been recovered. Twenty-eight species of ostracodes are described, two of them being new : Bairdia robinsoni nov. sp. and Rectobairdia conili nov. sp. The carbonates consist of bioclastic wackestones, bioclastic-peloid grainstones and algal bindstones. The depositional environment varied from an open marine shelf lagoon in the earliest Warnantian (Cf 6a zone) to very shallow lagoons with a restricted water circulation in the Cf 6a - ß zone. The extreme large size of the ostracode species recovered from the Cf 6a - ß zone is not characteristic of the very shallow lagoon environment. Extremely large ostracodes have also been recognized in other carbonate facies of Dinantian age

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 Fast, Memory-Efficient Alpha-Tree Algorithm using Flooding and Tree Size Estimation

The alpha-tree represents an image as hierarchical set of alpha-connected components. Computation of alpha-trees suffers from high computational and memory requirements compared with similar component tree algorithms such as max-tree. Here we introduce a novel alpha-tree algorithm using 1) a flooding algorithm for computational efficiency and 2) tree size estimation (TSE) for memory efficiency. In TSE, an exponential decay model was fitted to normalized tree sizes as a function of the normalized root mean squared deviation (NRMSD) of edge-dissimilarity distributions, and the model was used to estimate the optimum memory allocation size for alpha-tree construction. An experiment on 1256 images shows that our algorithm runs 2.27 times faster than Ouzounis and Soille's thanks to the flooding algorithm, and TSE reduced the average memory allocation of the proposed algorithm by 40.4%, eliminating unused allocated memory by 86.0% with a negligible computational cost

Spatially-Variant Directional Mathematical Morphology Operators Based on a Diffused Average Squared Gradient Field

International audienceThis paper proposes an approach for mathematical morphology operators whose structuring element can locally adapt its orientation across the pixels of the image. The orientation at each pixel is extracted by means of a diffusion process of the average squared gradient field. The resulting vector field, the average squared gradient vector flow, extends the orientation information from the edges of the objects to the homogeneous areas of the image. The provided orientation field is then used to perform a spatially variant filtering with a linear structuring element. Results of erosion, dilation, opening and closing spatially-variant on binary images prove the validity of this theoretical sound and novel approach

Impulsive noise removal from color images with morphological filtering

This paper deals with impulse noise removal from color images. The proposed noise removal algorithm employs a novel approach with morphological filtering for color image denoising; that is, detection of corrupted pixels and removal of the detected noise by means of morphological filtering. With the help of computer simulation we show that the proposed algorithm can effectively remove impulse noise. The performance of the proposed algorithm is compared in terms of image restoration metrics and processing speed with that of common successful algorithms.Comment: The 6th international conference on analysis of images, social networks, and texts (AIST 2017), 27-29 July, 2017, Moscow, Russi

Climbing: A Unified Approach for Global Constraints on Hierarchical Segmentation

International audienceThe paper deals with global constraints for hierarchical segmentations. The proposed framework associates, with an input image, a hierarchy of segmentations and an energy, and the subsequent optimization problem. It is the first paper that compiles the different global constraints and unifies them as Climbing energies. The transition from global optimization to local optimization is attained by the h-increasingness property, which allows to compare parent and child partition energies in hierarchies. The laws of composition of such energies are established and examples are given over the Berkeley Dataset for colour and texture segmentation

Hierarchical segmentation of complex structures

We present an unsupervised hierarchical segmentation algorithm for detection of complex heterogeneous image structures that are comprised of simpler homogeneous primitive objects. An initial segmentation step produces regions corresponding to primitive objects with uniform spectral content. Next, the transitions between neighboring regions are modeled and clustered. We assume that the clusters that are dense and large enough in this transition space can be considered as significant. Then, the neighboring regions belonging to the significant clusters are merged to obtain the next level in the hierarchy. The experiments show that the algorithm that iteratively clusters and merges region groups is able to segment high-level complex structures in a hierarchical manner. © 2010 IEEE

Optimal topological simplification of discrete functions on surfaces

We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance {\delta} from a given input function. The result is achieved by establishing a connection between discrete Morse theory and persistent homology. Our method completely removes homological noise with persistence less than 2{\delta}, constructively proving the tightness of a lower bound on the number of critical points given by the stability theorem of persistent homology in dimension two for any input function. We also show that an optimal solution can be computed in linear time after persistence pairs have been computed.Comment: 27 pages, 8 figure

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