Publications

Morphological hierarchical image decomposition based on Laplacian 0-crossings

Abstract

A method of text detection in natural images, to be turn into an effective embedded software on a mobile device, shall be both efficient and lightweight. We observed that a simple method based on the morphological Laplace operator can do the trick: we can construct in quasi-linear time a hierarchical image decomposition / simplification based on its 0-crossings, and search for some text in the resulting tree. Yet, for this decomposition to be sound, we need “0-crossings” to be Jordan curves, and to that aim, we rely on some discrete topology tools. Eventually, the hierarchical representation is the morphological tree of shapes of the Laplacian sign. Moreover, we provide an algorithm with linear time complexity to compute this representation. We expect that the proposed hierarchical representation can be useful in some applications other than text detection.

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Periodic area-of-motion characterization for bio-medical applications

Abstract

Many bio-medical applications involve the analysis of sequences for motion characterization. In this article, we consider 2D+t sequences where a particular motion (e.g. a blood flow) is associated with a specific area of the 2D image (e.g. an artery) but multiple motions may exist simultaneously in the same sequences (e.g. there may be several blood vessels present, each with their specific flow). The characterization of this type of motion typically involves first finding the areas where motion is present, followed by an analysis of these motions: speed, regularity, frequency, etc. In this article, we propose a methodology called “area-of-motion characterization” suitable for simultaneously detecting and characterizing areas where motion is present in a sequence. We can then classify this motion into consistent areas using unsupervised learning and produce directly usable metrics for various ap- plications. We illustrate this methodology for the analysis of cilia motion on ex-vivo human samples, and we apply and validate the same methodology for blood flow analysis in fish embryo.

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Programmatic manipulation of Common Lisp type specifiers

Abstract

In this article we contrast the use of the s-expression with the BDD (Binary Decision Diagram) as a data structure for programmatically manipulating Common Lisp type specifiers. The s-expression is the de facto standard surface syntax and also programmatic representation of the type specifier, but the BDD data structure offers advantages: most notably, type equivalence checks using s-expressions can be computationally intensive, whereas the type equivalence check using BDDs is a check for object identity. As an implementation and performance experiment, we define the notion of maximal disjoint type decomposition, and discuss implementations of algorithms to compute it: a brute force iteration, and as a tree reduction. The experimental implementations represent type specifiers by both aforementioned data structures, and we compare the performance observed in each approach.

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Analysis of algorithms calculating the maximal disjoint decomposition of a set

Abstract

In this article we demonstrate 4 algorithms for calculating the maximal disjoint decomposition of a given set of types. We discuss some advantages and disadvantages of each, and compare their performance. We extended currently known work to describe an efficient algorithm for manipulating binary decision diagrams representing types in a programming language which supports subtyping viewed as subsets.

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Contributions to LTL and $\omega$-automata for model checking

Abstract

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The MIT Lincoln Laboratory 2016 speaker recognition system

Abstract

This document presents the system submission for the group composed of MIT Lincoln Laboratory, Johns Hopkins University (JHU), Laboratoire de Recherche et de Développement de l’EPITA (LRDE) and Universidad Autónoma de Madrid (ATVS). The primary submission is a combination of four systems focused on i-vector systems. Two secondary submissions are also included

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A study of well-composedness in $n$-d

Abstract

Digitization of the real world using real sensors has many drawbacks; in particular, we loose “well-composedness” in the sense that two digitized objects can be connected or not depending on the connectivity we choose in the digital image, leading then to ambiguities. Furthermore, digitized images are arrays of numerical values, and then do not own any topology by nature, contrary to our usual modeling of the real world in mathematics and in physics. Loosing all these properties makes difficult the development of algorithms which are “topologically correct” in image processing: e.g., the computation of the tree of shapes needs the representation of a given image to be continuous and well-composed; in the contrary case, we can obtain abnormalities in the final result. Some well-composed continuous representations already exist, but they are not in the same time $n$-dimensional and self-dual. In fact, $n$-dimensionality is crucial since usual signals are more and more 3-dimensional (like 2D videos) or 4-dimensional (like 4D Computerized Tomography-scans), and self-duality is necessary when a same image can contain different objects with different contrasts. We developed then a new way to make images well-composed by interpolation in a self-dual way and in $n$-D; followed with a span-based immersion, this interpolation becomes a self-dual continuous well-composed representation of the initial $n$-D signal. This representation benefits from many strong topological properties: it verifies the intermediate value theorem, the boundaries of any threshold set of the representation are disjoint union of discrete surfaces, and so on.

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Estimating the number of endmembers to use in spectral unmixing of hyperspectral data with collaborative sparsity

Abstract

Spectral Umixing (SU) in hyperspectral remote sensing aims at recovering the signatures of the pure materials in the scene (endmembers) and their abundances in each pixel of the image. The usual SU chain does not take spectral variability (SV) into account, and relies on the estimation of the Intrinsic Dimensionality (ID) of the data, related to the number of endmembers (NOE) to use. However, the ID can be significantly overestimated in difficult scenarios, and sometimes does not correspond to the desired scale and application dependent NOE. Spurious endmembers are then frequently extracted and included in the model. We propose an algorithm for SU incorporating SV, using collaborative sparsity to discard the least explicative endmembers in the whole image. We compute an algorithmic regularization path for this problem to select the optimal set of endmembers using a statistical criterion. Results on simulated and real data show the interest of the approach.

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Monads in Common Lisp

Abstract

In this article we explain monads so they can be understood to the Lisp programmer. We base the explanation on a very clean explanation presented in the Scala programming language. We then proceed to re-present the concepts using mostly simple Common Lisp concepts. We do not attempt to justify the motivation behind the definitions, and we do not attempt to give any examples of applications. Most notably, we do not attempt to explain the connection monads have to modeling side effects.

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Finding maximal common joins in a DAG

Abstract

Given a directed acyclic graph (DAG) and two arbitrary nodes, find maximal common joins of the two nodes. In this technical report I suggest an algorithm for efficiently calculating the minimal set of nodes which derive from a pair of nodes.

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