A Learning Framework for Morphological Operators using Counter-Harmonic Mean

We present a novel framework for learning morphological operators using counter-harmonic mean. It combines concepts from morphology and convolutional neural networks. A thorough experimental validation analyzes basic morphological operators dilation and erosion, opening and closing, as well as the much more complex top-hat transform, for which we report a real-world application from the steel industry. Using online learning and stochastic gradient descent, our system learns both the structuring element and the composition of operators. It scales well to large datasets and online settings.Comment: Submitted to ISMM'1

Morphological bilateral filtering

International audienceA current challenging topic in mathematical morphology is the construction of locally adaptive operators; i.e., structuring functions that are dependent on the input image itself at each position. Development of spatially-variant filtering is well established in the theory and practice of Gaussian filtering. The aim of the first part of the paper is to study how to generalize these convolution-based approaches in order to introduce adaptive nonlinear filters that asymptotically correspond to spatially-variant morphological dilation and erosion. In particular, starting from the bilateral filtering framework and using the notion of counter-harmonic mean, our goal is to propose a new low complexity approach to define spatially-variant bilateral structuring functions. Then, in the second part of the paper, an original formulation of spatially-variant flat morphological filters is proposed, where the adaptive structuring elements are obtained by thresholding the bilateral structuring functions. The methodological results of the paper are illustrated with various comparative examples

Generalised morphological image diffusion

International audienceRelationships between linear and morphological scale-spaces have been considered by various previous works. The aim of this paper is to study how to generalise the diffusion-based approaches in order to introduce nonlinear filters whose effects mimic the asymmetric behaviour of morphological dilation and erosion, as well as other evolved morphological filters. A methodology based on the counter-harmonic mean is adopted here. Details of numerical implementation are discussed and results are provided to illustrate the various studied cases: isotropic, nonlinear and coherence-enhancing diffusion. We also found a new way to derive the classical link between Gaussian scale-space and dilation/erosion scale-spaces based on quadratic structuring functions. We have included some preliminary applications of the generalised morphological diffusion to solve image processing problems such as denoising and image enhancement in the case of asymmetric bright/dark image properties

Learning morphological operators for depth completion

Depth images generated by direct projection of LiDAR point clouds on the image plane suffer from a great level of sparsity which is difficult to interpret by classical computer vision algorithms. We propose a method for completing sparse depth images in a semantically accurate manner by training a novel morphological neural network. Our method approximates morphological operations by Contraharmonic Mean Filter layers which are easily trained in a contemporary deep learning framework. An early fusion U-Net architecture then combines dilated depth channels and RGB using multi-scale processing. Using a large scale RGBD dataset we are able to learn the optimal morphological and convolutional filter shapes that produce an accurate and fully sampled depth image at the output. Independent experimental evaluation confirms that our method outperforms classical image restoration techniques as well as current state-of-the-art neural networks. The resulting depth images preserve object boundaries and can easily be used to augment various tasks in intelligent vehicles perception systems

Order out of Randomness : Self-Organization Processes in Astrophysics

Self-organization is a property of dissipative nonlinear processes that are governed by an internal driver and a positive feedback mechanism, which creates regular geometric and/or temporal patterns and decreases the entropy, in contrast to random processes. Here we investigate for the first time a comprehensive number of 16 self-organization processes that operate in planetary physics, solar physics, stellar physics, galactic physics, and cosmology. Self-organizing systems create spontaneous {\sl order out of chaos}, during the evolution from an initially disordered system to an ordered stationary system, via quasi-periodic limit-cycle dynamics, harmonic mechanical resonances, or gyromagnetic resonances. The internal driver can be gravity, rotation, thermal pressure, or acceleration of nonthermal particles, while the positive feedback mechanism is often an instability, such as the magneto-rotational instability, the Rayleigh-B\'enard convection instability, turbulence, vortex attraction, magnetic reconnection, plasma condensation, or loss-cone instability. Physical models of astrophysical self-organization processes involve hydrodynamic, MHD, and N-body formulations of Lotka-Volterra equation systems.Comment: 61 pages, 38 Figure

Efficient Monte Carlo methods for simulating diffusion-reaction processes in complex systems

We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to study various probabilistic characteristics (harmonic measure, first passage/exit time distribution, reaction rates, search times and strategies, etc.) and to solve the related partial differential equations. The adaptive character and flexibility of FRWs make them particularly efficient for simulating diffusive processes in porous, multiscale, heterogeneous, disordered or irregularly-shaped media

Fluorescence microscopy tensor imaging representations for large-scale dataset analysis

Understanding complex biological systems requires the system-wide characterization of cellular and molecular features. Recent advances in optical imaging technologies and chemical tissue clearing have facilitated the acquisition of whole-organ imaging datasets, but automated tools for their quantitative analysis and visualization are still lacking. We have here developed a visualization technique capable of providing whole-organ tensor imaging representations of local regional descriptors based on fluorescence data acquisition. This method enables rapid, multiscale, analysis and virtualization of large-volume, high-resolution complex biological data while generating 3D tractographic representations. Using the murine heart as a model, our method allowed us to analyze and interrogate the cardiac microvasculature and the tissue resident macrophage distribution and better infer and delineate the underlying structural network in unprecedented detail

Large-scale Geometric Data Decomposition, Processing and Structured Mesh Generation

Mesh generation is a fundamental and critical problem in geometric data modeling and processing. In most scientific and engineering tasks that involve numerical computations and simulations on 2D/3D regions or on curved geometric objects, discretizing or approximating the geometric data using a polygonal or polyhedral meshes is always the first step of the procedure. The quality of this tessellation often dictates the subsequent computation accuracy, efficiency, and numerical stability. When compared with unstructured meshes, the structured meshes are favored in many scientific/engineering tasks due to their good properties. However, generating high-quality structured mesh remains challenging, especially for complex or large-scale geometric data. In industrial Computer-aided Design/Engineering (CAD/CAE) pipelines, the geometry processing to create a desirable structural mesh of the complex model is the most costly step. This step is semi-manual, and often takes up to several weeks to finish. Several technical challenges remains unsolved in existing structured mesh generation techniques. This dissertation studies the effective generation of structural mesh on large and complex geometric data. We study a general geometric computation paradigm to solve this problem via model partitioning and divide-and-conquer. To apply effective divide-and-conquer, we study two key technical components: the shape decomposition in the divide stage, and the structured meshing in the conquer stage. We test our algorithm on vairous data set, the results demonstrate the efficiency and effectiveness of our framework. The comparisons also show our algorithm outperforms existing partitioning methods in final meshing quality. We also show our pipeline scales up efficiently on HPC environment