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.

Hierarchies, such as the tree of shapes, are popular representations for image simplification and segmentation thanks to their multiscale structures. Selecting meaningful level lines (boundaries of shapes) yields to simplify image while preserving intact salient structures. Many image simplification and segmentation methods are driven by the optimization of an energy functional, for instance the celebrated Mumford-Shah functional. In this paper, we propose an efficient approach to hierarchical image simplification and segmentation based on the minimization of the piecewise-constant Mumford-Shah functional. This method conforms to the current trend that consists in producing hierarchical results rather than a unique partition. Contrary to classical approaches which compute optimal hierarchical segmentations from an input hierarchy of segmentations, we rely on the tree of shapes, a unique and well-defined representation equivalent to the image. Simply put, we compute for each level line of the image an attribute function that characterizes its persistence under the energy minimization. Then we stack the level lines from meaningless ones to salient ones through a saliency map based on extinction values defined on the tree-based shape space. Qualitative illustrations and quantitative evaluation on Weizmann segmentation evaluation database demonstrate the state-of-the-art performance of our method.

Current text segmentation evaluation protocols are often incapable of properly handling different scenarios (broken/merged/partial characters). This leads to scores that incorrectly reflect the segmentation accuracy. In this article we propose a new evaluation scheme that overcomes most of the existent drawbacks by extending the EvaLTex protocol (initially designed to evaluate text detection at region level). This new unified platform has numerous advantages: it is able to evaluate a text understanding system at every detection stage and granularity level (paragraph/line/word and now character) by using the same metrics and matching rules; it is robust to all segmentation scenarios; it provides a qualitative and quantitative evaluation and a visual score representation that captures the whole behavior of a segmentation algorithm. Experimental results on nine segmentation algorithms using different evaluation frameworks are also provided to emphasize the interest of our method.

We present an algorithm to build an automaton from a rational expression. This approach introduces support for extended weighted expressions. Inspired by derived-term based algorithms, its core relies on a different construct, rational expansions. We introduce an inductive algorithm to compute the expansion of an expression from which the automaton follows. This algorithm is independent of the size of the alphabet, and actually even supports infinite alphabets. It can easily be accommodated to generate deterministic (weighted) automata. These constructs are implemented in Vcsn, a free-software platform dedicated to weighted automata and rational expressions.

Checking liveness properties with partial-order reductions requires a cycle proviso to ensure that an action cannot be postponed forever. The proviso forces each cycle to contain at least one fully expanded state. We present new heuristics to select which state to expand, hoping to reduce the size of the resulting graph. The choice of the state to expand is done when encountering a <i>dangerous</i> edge. Almost all existing provisos expand the source of this edge, while this paper also explores the expansion of the destination and the use of SCC-based information.

We present Spot 2.0, a C++ library with Python bindings and an assortment of command-line tools designed to manipulate LTL and $\omega$-automata in batch. New automata-manipulation tools were introduced in Spot 2.0; they support arbitrary acceptance conditions, as expressible in the Hanoi Omega Automaton format. Besides being useful to researchers who have automata to process, its Python bindings can also be used in interactive environments to teach $\omega$-automata and model checking.

The progress of magnetic resonance imaging (MRI) allows for a precise exploration of the brain of premature infants at term equivalent age. The so-called DEHSI (diffuse excessive high signal intensity) of the white matter of premature brains remains a challenging issue in terms of definition, and thus of interpretation. We propose a semi-automatic detection and quantification method of white matter hyperintensities in MRI relying on morphological operators and max-tree representations, which constitutes a powerful tool to help radiologists to improve their interpretation. Results show better reproducibility and robustness than interactive segmentation.

Satellite image classification is a key task used in remote sensing for the automatic interpretation of a large amount of information. Today there exist many types of classification algorithms using advanced image processing methods enhancing the classification accuracy rate. One of the best state-of-the-art methods which improves significantly the classification of complex scenes relies on Self-Dual Attribute Profiles (SDAPs). In this approach, the underlying representation of an image is the Tree of Shapes, which encodes the inclusion of connected components of the image. The SDAP computes for each pixel a vector of attributes providing a local multiscale representation of the information and hence leading to a fine description of the local structures of the image. Instead of performing a pixel-wise classification on features extracted from the Tree of Shapes, it is proposed to directly classify its nodes. Extending a specific interactive segmentation algorithm enables it to deal with the multi-class classification problem. The method does not involve any statistical learning and it is based entirely on morphological information related to the tree. Consequently, a very simple and effective region-based classifier relying on basic attributes is presented.

We introduce (weighted) rational expressions to denote series over Cartesian products of monoids. To this end, we propose the operator $\mid$ to build multitape expressions such as $(a^+\mid x + b^+\mid y)^*$. We define expansions, which generalize the concept of derivative of a rational expression, but relieved from the need of a free monoid. We propose an algorithm based on expansions to build multitape automata from multitape expressions.

Connected filters are well-known for their good contour preservation property. A popular implementation strategy relies on tree-based image representations: for example, one can compute an attribute characterizing the connected component represented by each node of the tree and keep only the nodes for which the attribute is sufficiently high. This operation can be seen as a thresholding of the tree, seen as a graph whose nodes are weighted by the attribute. Rather than being satisfied with a mere thresholding, we propose to expand on this idea, and to apply connected filters on this latest graph. Consequently, the filtering is performed not in the space of the image, but in the space of shapes built from the image. Such a processing of shape-space filtering is a generalization of the existing tree-based connected operators. Indeed, the framework includes the classical existing connected operators by attributes. It also allows us to propose a class of novel connected operators from the leveling family, based on non-increasing attributes. Finally, we also propose a new class of connected operators that we call morphological <i>shapings</i>. Some illustrations and quantitative evaluations demonstrate the usefulness and robustness of the proposed shape-space filters.