Brain-inspired automated visual object discovery and detection

Despite significant recent progress, machine vision systems lag considerably behind their biological counterparts in performance, scalability, and robustness. A distinctive hallmark of the brain is its ability to automatically discover and model objects, at multiscale resolutions, from repeated exposures to unlabeled contextual data and then to be able to robustly detect the learned objects under various nonideal circumstances, such as partial occlusion and different view angles. Replication of such capabilities in a machine would require three key ingredients: (i) access to large-scale perceptual data of the kind that humans experience, (ii) flexible representations of objects, and (iii) an efficient unsupervised learning algorithm. The Internet fortunately provides unprecedented access to vast amounts of visual data. This paper leverages the availability of such data to develop a scalable framework for unsupervised learning of object prototypes—brain-inspired flexible, scale, and shift invariant representations of deformable objects (e.g., humans, motorcycles, cars, airplanes) comprised of parts, their different configurations and views, and their spatial relationships. Computationally, the object prototypes are represented as geometric associative networks using probabilistic constructs such as Markov random fields. We apply our framework to various datasets and show that our approach is computationally scalable and can construct accurate and operational part-aware object models much more efficiently than in much of the recent computer vision literature. We also present efficient algorithms for detection and localization in new scenes of objects and their partial views

Maximal Independent Sets for Pooling in Graph Neural Networks

Convolutional Neural Networks (CNNs) have enabled major advances in image classification through convolution and pooling. In particular, image pooling transforms a connected discrete lattice into a reduced lattice with the same connectivity and allows reduction functions to consider all pixels in an image. However, there is no pooling that satisfies these properties for graphs. In fact, traditional graph pooling methods suffer from at least one of the following drawbacks: Graph disconnection or overconnection, low decimation ratio, and deletion of large parts of graphs. In this paper, we present three pooling methods based on the notion of maximal independent sets that avoid these pitfalls. Our experimental results confirm the relevance of maximal independent set constraints for graph pooling

Machine Learning for Instance Segmentation

Volumetric Electron Microscopy images can be used for connectomics, the study of brain connectivity at the cellular level. A prerequisite for this inquiry is the automatic identification of neural cells, which requires machine learning algorithms and in particular efficient image segmentation algorithms. In this thesis, we develop new algorithms for this task. In the first part we provide, for the first time in this field, a method for training a neural network to predict optimal input data for a watershed algorithm. We demonstrate its superior performance compared to other segmentation methods of its category. In the second part, we develop an efficient watershed-based algorithm for weighted graph partitioning, the \emph{Mutex Watershed}, which uses negative edge-weights for the first time. We show that it is intimately related to the multicut and has a cutting edge performance on a connectomics challenge. Our algorithm is currently used by the leaders of two connectomics challenges. Finally, motivated by inpainting neural networks, we create a method to learn the graph weights without any supervision

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

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

From spline wavelet to sampling theory on circulant graphs and beyond– conceiving sparsity in graph signal processing

Graph Signal Processing (GSP), as the field concerned with the extension of classical signal processing concepts to the graph domain, is still at the beginning on the path toward providing a generalized theory of signal processing. As such, this thesis aspires to conceive the theory of sparse representations on graphs by traversing the cornerstones of wavelet and sampling theory on graphs. Beginning with the novel topic of graph spline wavelet theory, we introduce families of spline and e-spline wavelets, and associated filterbanks on circulant graphs, which lever- age an inherent vanishing moment property of circulant graph Laplacian matrices (and their parameterized generalizations), for the reproduction and annihilation of (exponen- tial) polynomial signals. Further, these families are shown to provide a stepping stone to generalized graph wavelet designs with adaptive (annihilation) properties. Circulant graphs, which serve as building blocks, facilitate intuitively equivalent signal processing concepts and operations, such that insights can be leveraged for and extended to more complex scenarios, including arbitrary undirected graphs, time-varying graphs, as well as associated signals with space- and time-variant properties, all the while retaining the focus on inducing sparse representations. Further, we shift from sparsity-inducing to sparsity-leveraging theory and present a novel sampling and graph coarsening framework for (wavelet-)sparse graph signals, inspired by Finite Rate of Innovation (FRI) theory and directly building upon (graph) spline wavelet theory. At its core, the introduced Graph-FRI-framework states that any K-sparse signal residing on the vertices of a circulant graph can be sampled and perfectly reconstructed from its dimensionality-reduced graph spectral representation of minimum size 2K, while the structure of an associated coarsened graph is simultaneously inferred. Extensions to arbitrary graphs can be enforced via suitable approximation schemes. Eventually, gained insights are unified in a graph-based image approximation framework which further leverages graph partitioning and re-labelling techniques for a maximally sparse graph wavelet representation.Open Acces

Formal Verification of Industrial Software and Neural Networks

Software ist ein wichtiger Bestandteil unsere heutige Gesellschaft. Da Software vermehrt in sicherheitskritischen Bereichen angewandt wird, müssen wir uns auf eine korrekte und sichere Ausführung verlassen können. Besonders eingebettete Software, zum Beispiel in medizinischen Geräten, Autos oder Flugzeugen, muss gründlich und formal geprüft werden. Die Software solcher eingebetteten Systeme kann man in zwei Komponenten aufgeteilt. In klassische (deterministische) Steuerungssoftware und maschinelle Lernverfahren zum Beispiel für die Bilderkennung oder Kollisionsvermeidung angewandt werden. Das Ziel dieser Dissertation ist es den Stand der Technik bei der Verifikation von zwei Hauptkomponenten moderner eingebetteter Systeme zu verbessern: in C/C++ geschriebene Software und neuronalen Netze. Für beide Komponenten wird das Verifikationsproblem formal definiert und neue Verifikationsansätze werden vorgestellt

Stochastic graphlet embedding

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordGraph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semistructured data as graphs where nodes correspond to primitives (parts, interest points, and segments) and edges characterize the relationships between these primitives. However, these nonvectorial graph data cannot be straightforwardly plugged into off-the-shelf machine learning algorithms without a preliminary step of - explicit/implicit - graph vectorization and embedding. This embedding process should be resilient to intraclass graph variations while being highly discriminant. In this paper, we propose a novel high-order stochastic graphlet embedding that maps graphs into vector spaces. Our main contribution includes a new stochastic search procedure that efficiently parses a given graph and extracts/samples unlimitedly high-order graphlets. We consider these graphlets, with increasing orders, to model local primitives as well as their increasingly complex interactions. In order to build our graph representation, we measure the distribution of these graphlets into a given graph, using particular hash functions that efficiently assign sampled graphlets into isomorphic sets with a very low probability of collision. When combined with maximum margin classifiers, these graphlet-based representations have a positive impact on the performance of pattern comparison and recognition as corroborated through extensive experiments using standard benchmark databases.Agence Nationale de la Recherche (ANR