Connected operators based on region-tree pruning strategies

This paper discusses region-based representations useful to create connected operators. The filtering approach involves three steps: 1) a region tree representation of the input image is constructed; 2) the simplification is obtained by pruning the tree; and 3) and output image is constructed from the pruned tree. The paper focuses in particular on the pruning strategies that can be used depending of the increasing of the simplification criteria.Peer ReviewedPostprint (published version

Optimum graph cuts for pruning binary partition trees of polarimetric SAR images

This paper investigates several optimum graph-cut techniques for pruning binary partition trees (BPTs) and their usefulness for the low-level processing of polarimetric synthetic aperture radar (PolSAR) images. BPTs group pixels to form homogeneous regions, which are hierarchically structured by inclusion in a binary tree. They provide multiple resolutions of description and easy access to subsets of regions. Once constructed, BPTs can be used for a large number of applications. Many of these applications consist in populating the tree with a specific feature and in applying a graph cut called pruning to extract a partition of the space. In this paper, different pruning examples involving the optimization of a global criterion are discussed and analyzed in the context of PolSAR images for segmentation. Through the objective evaluation of the resulting partitions by means of precision-and-recall-for-boundaries curves, the best pruning technique is identified, and the influence of the tree construction on the performances is assessed.Peer ReviewedPostprint (author's final draft

Connected operators for sprite creation and layered representation of image sequences

This paper proposes and discusses the use of motion-oriented connected operators for sprite creation. Motion-oriented connected operators are tools allowing the simplification of frames by removing objects that do not follow a given motion. They combine features of filtering and segmentation tools. They are, however, less computationally expensive than most motion-oriented segmentation algorithms. In this paper, we show how they can be used to efficiently remove outliers with respect to the dominant motion and to create layered representation of sequences.Peer ReviewedPostprint (published version

Robust motion estimation using connected operators

This paper discusses the use of connected operators for robust motion estimation The proposed strategy involves a motion estimation step extracting the dominant motion and a ltering step relying on connected operators that remove objects that do not fol low the dominant motion. These two steps are iterated in order to obtain an accurate motion estimation and a precise de nition of the objects fol lowing this motion This strategy can be applied on the entire frame or on individual connected components As a result the complete motion oriented segmentation and motion estimation of the frame can be achievedPeer ReviewedPostprint (published version

Self correction requires Energy Barrier for Abelian quantum doubles

We rigorously establish an Arrhenius law for the mixing time of quantum doubles based on any Abelian group $\mathbb{Z}_d$. We have made the concept of the energy barrier therein mathematically well-defined, it is related to the minimum energy cost the environment has to provide to the system in order to produce a generalized Pauli error, maximized for any generalized Pauli errors, not only logical operators. We evaluate this generalized energy barrier in Abelian quantum double models and find it to be a constant independent of system size. Thus, we rule out the possibility of entropic protection for this broad group of models.Comment: 18 pages, 6 figure

Remote Sensing Image Classification Using Attribute Filters Defined over the Tree of Shapes

International audience—Remotely sensed images with very high spatial resolution provide a detailed representation of the surveyed scene with a geometrical resolution that at the present can be up to 30 cm (WorldView-3). A set of powerful image processing operators have been defined in the mathematical morphology framework. Among those, connected operators (e.g., attribute filters) have proven their effectiveness in processing very high resolution images. Attribute filters are based on attributes which can be efficiently implemented on tree-based image representations. In this work, we considered the definition of min, max, direct and subtractive filter rules for the computation of attribute filters over the tree of shapes representation. We study their performance on the classification of remotely sensed images. We compare the classification results over the tree of shapes with the results obtained when the same rules are applied on the component trees. The random forest is used as a baseline classifier and the experiments are conducted using multispectral data sets acquired by QuickBird and IKONOS sensors over urban areas

A Robust Parsing Algorithm For Link Grammars

In this paper we present a robust parsing algorithm based on the link grammar formalism for parsing natural languages. Our algorithm is a natural extension of the original dynamic programming recognition algorithm which recursively counts the number of linkages between two words in the input sentence. The modified algorithm uses the notion of a null link in order to allow a connection between any pair of adjacent words, regardless of their dictionary definitions. The algorithm proceeds by making three dynamic programming passes. In the first pass, the input is parsed using the original algorithm which enforces the constraints on links to ensure grammaticality. In the second pass, the total cost of each substring of words is computed, where cost is determined by the number of null links necessary to parse the substring. The final pass counts the total number of parses with minimal cost. All of the original pruning techniques have natural counterparts in the robust algorithm. When used together with memoization, these techniques enable the algorithm to run efficiently with cubic worst-case complexity. We have implemented these ideas and tested them by parsing the Switchboard corpus of conversational English. This corpus is comprised of approximately three million words of text, corresponding to more than 150 hours of transcribed speech collected from telephone conversations restricted to 70 different topics. Although only a small fraction of the sentences in this corpus are "grammatical" by standard criteria, the robust link grammar parser is able to extract relevant structure for a large portion of the sentences. We present the results of our experiments using this system, including the analyses of selected and random sentences from the corpus.Comment: 17 pages, compressed postscrip

Multifractals, Mumford curves, and Eternal Inflation

We relate the Eternal Symmetree model of Harlow, Shenker, Stanford, and Susskind to constructions of stochastic processes arising from quantum statistical mechanical systems on Cuntz--Krieger algebras. We extend the eternal inflation model from the Bruhat--Tits tree to quotients by p-adic Schottky groups, again using quantum statistical mechanics on graph algebras.Comment: 19 pages, LaTeX, 4 pdf figure