110,127 research outputs found

    Measuring Similarity between Wavelet Function and Transient in a Signal with Symmetric Distance Coefficient

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    Wavelet transform has been developed and applied in various areas of science and engineering. It offers better signal processing capabilities due to the existence of a large number of wavelet functions. The superiority comes with a requirement of methods to select a proper wavelet function for each signal or application. Selection methods based on signal properties are not always applicable due to the lack of mathematical definition of most analyzed signals. Wavelet function can be selected based on its shape similarity to interested transient in input signal. The selection method is subjective since there is no quantified parameter to measure this similarity. This paper introduces a new parameter, symmetric distance coefficient (SDC) to measure similarity between wavelet function and transient in a signal. It is based on a fact that wavelet coefficients of a transient that has similar shape and similar time support to a wavelet function are always symmetric. The parameter measures similarity by measuring the degree of symmetry in wavelet coefficients. The paper also reports an experiment to demonstrate procedures to measure this similarity using SDC

    ALGORITHMS FOR ADJUSTMENT OF SYMMETRY AXIS FOUND FOR 2D SHAPES BY THE SKELETON COMPARISON METHOD

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    Reflection symmetry detection for 2D shapes is a well-known task in Computer Vision, but there is a limited number of efficient and effective methods for its solution. Our previously proposed approach based on pair-wise comparison of sub-sequences of skeleton primitives finds the axis of symmetry within few seconds. In order to evaluate the value of symmetry relative to the found axis we use the Jaccard similarity measure. It is applied to the pixels subsets of a shape which are split by the axis. Often an axis found by the skeleton comparison method diverges more or less from the ground-truth axis found by the method of exhaustive search among all the potential candidates. That is why the algorithms that allow adjusting the axis found by the fast skeleton method are proposed. They are based on the idea of searching the axis which is located near the seed skeleton axis and has greater Jaccard similarity measure. The experimental study on the ”Flavia” and ”Butterflies” datasets shows that proposed algorithms find the ground-truth axis (or the axis which has slightly less Jaccard similarity value than the ground-truth axis) in near real time. It is considerably faster than any of the optimized brute-force methods

    Disconnected Skeleton: Shape at its Absolute Scale

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    We present a new skeletal representation along with a matching framework to address the deformable shape recognition problem. The disconnectedness arises as a result of excessive regularization that we use to describe a shape at an attainably coarse scale. Our motivation is to rely on the stable properties of the shape instead of inaccurately measured secondary details. The new representation does not suffer from the common instability problems of traditional connected skeletons, and the matching process gives quite successful results on a diverse database of 2D shapes. An important difference of our approach from the conventional use of the skeleton is that we replace the local coordinate frame with a global Euclidean frame supported by additional mechanisms to handle articulations and local boundary deformations. As a result, we can produce descriptions that are sensitive to any combination of changes in scale, position, orientation and articulation, as well as invariant ones.Comment: The work excluding {\S}V and {\S}VI has first appeared in 2005 ICCV: Aslan, C., Tari, S.: An Axis-Based Representation for Recognition. In ICCV(2005) 1339- 1346.; Aslan, C., : Disconnected Skeletons for Shape Recognition. Masters thesis, Department of Computer Engineering, Middle East Technical University, May 200

    The Nature of the Chemical Process. 1. Symmetry Evolution - Revised Information Theory, Similarity Principle and Ugly Symmetry

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    Three laws of information theory have been proposed. Labeling by introducing nonsymmetry and formatting by introducing symmetry are defined. The function L (L=lnw, w is the number of microstates, or the sum of entropy and information, L=S+I) of the universe is a constant (the first law of information theory). The entropy S of the universe tends toward a maximum (the second law law of information theory). For a perfect symmetric static structure, the information is zero and the static entropy is the maximum (the third law law of information theory). Based on the Gibbs inequality and the second law of the revised information theory we have proved the similarity principle (a continuous higher similarity-higher entropy relation after the rejection of the Gibbs paradox) and proved the Curie-Rosen symmetry principle (a higher symmetry-higher stability relation) as a special case of the similarity principle. Some examples in chemical physics have been given. Spontaneous processes of all kinds of molecular interaction, phase separation and phase transition, including symmetry breaking and the densest molecular packing and crystallization, are all driven by information minimization or symmetry maximization. The evolution of the universe in general and evolution of life in particular can be quantitatively considered as a series of symmetry breaking processes. The two empirical rules - similarity rule and complementarity rule - have been given a theoretical foundation. All kinds of periodicity in space and time are symmetries and contribute to the stability. Symmetry is beautiful because it renders stability. However, symmetry is in principle ugly because it is associated with information loss.Comment: 29 pages, 14 figure

    On Nonrigid Shape Similarity and Correspondence

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    An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape comparison. Here, we explore the applicability of related shape similarity measures to the problem of shape correspondence, adopting spectral type distances. We propose to evaluate the spectral kernel distance, the spectral embedding distance and the novel spectral quasi-conformal distance, comparing the manifolds from different viewpoints. By matching the shapes in the spectral domain, important attributes of surface structure are being aligned. For the purpose of testing our ideas, we introduce a fully automatic framework for finding intrinsic correspondence between two shapes. The proposed method achieves state-of-the-art results on the Princeton isometric shape matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks

    Categorical invariance and structural complexity in human concept learning

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    An alternative account of human concept learning based on an invariance measure of the categorical\ud stimulus is proposed. The categorical invariance model (CIM) characterizes the degree of structural\ud complexity of a Boolean category as a function of its inherent degree of invariance and its cardinality or\ud size. To do this we introduce a mathematical framework based on the notion of a Boolean differential\ud operator on Boolean categories that generates the degrees of invariance (i.e., logical manifold) of the\ud category in respect to its dimensions. Using this framework, we propose that the structural complexity\ud of a Boolean category is indirectly proportional to its degree of categorical invariance and directly\ud proportional to its cardinality or size. Consequently, complexity and invariance notions are formally\ud unified to account for concept learning difficulty. Beyond developing the above unifying mathematical\ud framework, the CIM is significant in that: (1) it precisely predicts the key learning difficulty ordering of\ud the SHJ [Shepard, R. N., Hovland, C. L.,&Jenkins, H. M. (1961). Learning and memorization of classifications.\ud Psychological Monographs: General and Applied, 75(13), 1-42] Boolean category types consisting of three\ud binary dimensions and four positive examples; (2) it is, in general, a good quantitative predictor of the\ud degree of learning difficulty of a large class of categories (in particular, the 41 category types studied\ud by Feldman [Feldman, J. (2000). Minimization of Boolean complexity in human concept learning. Nature,\ud 407, 630-633]); (3) it is, in general, a good quantitative predictor of parity effects for this large class of\ud categories; (4) it does all of the above without free parameters; and (5) it is cognitively plausible (e.g.,\ud cognitively tractable)
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