110,127 research outputs found
Measuring Similarity between Wavelet Function and Transient in a Signal with Symmetric Distance Coefficient
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
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
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
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
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
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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