Representation of Signals by Local Symmetry Decomposition

In this paper we propose a segmentation of finite support sequences based on the even/odd decomposition of a signal. The objective is to find a more compact representation of information. To this aim, the paper starts to generalize the even/odd decomposition by concentrating the energy on either the even or the odd part by optimally placing the centre of symmetry. Local symmetry intervals are thus located. The sequence segmentation is further processed by applying an iterative growth on the candidate segments to remove any overlapping portions. Experimental results show that the set of segments can be more eficiently compressed with respect to the DCT transformation of the entire sequence, which corresponds to the near optimal KLT transform of the data chosen for the experiment

On reflection symmetry in natural images

Many new symmetry detection algorithms have been recently developed, thanks to an interest revival on computational symmetry for computer graphics and computer vision applications. Notably, in 2013 the IEEE CVPR Conference organized a dedicated workshop and an accompanying symmetry detection competition. In this paper we propose an approach for symmetric object detection that is based both on the computation of a symmetry measure for each pixel and on saliency. The symmetry value is obtained as the energy balance of the even-odd decomposition of a patch w.r.t. each possible axis. The candidate symmetry axes are then identified through the localization of peaks along the direction perpendicular to each considered axis orientation. These found candidate axes are finally evaluated through a confidence measure that also allow removing redundant detected symmetries. The obtained results within the framework adopted in the aforementioned competition show significant performance improvement

Even/odd decomposition made sparse: A fingerprint to hidden patterns

The very fundamental operation of even/odd decomposition is at the core of some of the simplest information representation and signal processing tasks. So far most of its use has been for rearranging data to provide fast implementations of various types of transforms (Fourier, DCT, …) or for achieving elementary data transformation, such as the Walsh–Hadamard transform. This work proposes to look into the decomposition framework to obtain a richer perspective. In the context of an iterated even/odd decomposition, it is possible to pinpoint intermediate layered levels of symmetries which cannot be easily captured in the original data. In addition this determines a hierarchical fingerprinting for any sort of continuous finite support analog signal or for any discrete-time sequence which may turn out useful in several recognition or categorization tasks. It also may help to achieve sparsity within a natural hierarchical framework, which could be easily extended for many other types of orthogonal transformations. This paper also suggests a global measure of the energy imbalance across the hierarchy of the decomposition to capture the overall fingerprinting of this interpretation

Image symmetries: The right balance between evenness and perception

A recent and fascinating interest in computational symmetry for computer vision and computer graphics applications has led to a remarkable realization of new symmetry detection algorithms. Such a concern is culminated in a symmetry detection competition as a workshop affiliated with the 2011 and 2013 CVPR Conferences. In this paper, we propose a method based on the computation of the symmetry level associated to each pixel. Such a value is determined through the energy balance of the even/odd decomposition of a patch with respect to a central axis (which is equivalent to estimate the middle point of a row-wise convolution). Peaks localization along the perpendicular direction of each angle allows to identify possible symmetry axes. The evaluation of a feature based on gradient information allows to establish a classification confidence for each detected axis. By adopting the aforementioned rigorous validation framework, the proposed method indicates significant performance increase

A tool for the quantification of radial neo-vessels in chick chorioallantoic membrane angiogenic assays

Angiogenesis, the process of new blood vessels formation, plays a key role in different physiological and pathological conditions and it is considered a promising target for the development of new anti-inflammatory and anti-tumor therapies. Several assays have been developed to mimic the angiogenic process in vitro and in vivo. Here we propose a technique for the quantification of the pro-angiogenic or anti-angiogenic responses induced by different molecules when implanted in vivo on the chick embryo chorioallantoic membrane (CAM). At day 11 of development CAM is completely vascularized and neo-vessels induced by exogenous molecules converge radially to the implant. Our algorithm is an effective and rapid tool to characterize molecules endowed with proor anti-angiogenic effects by means of the quantification of the vessels present in the CAM macroscopic images. Based on conventional and dedicated image morphology tools, the proposed technique is able to discriminate radial from non-radial vessels, excluding the last ones from the count

Human Mutated MYOT and CRYAB Genes Cause a Myopathic Phenotype in Zebrafish

Myofibrillar myopathies (MFMs) are a group of hereditary neuromuscular disorders sharing common histological features, such as myofibrillar derangement, Z-disk disintegration, and accumulation of degradation products into protein aggregates. They are caused by mutations in several genes that encode either structural proteins or molecular chaperones. Nevertheless, the mechanisms by which mutated genes result in protein aggregation are still unknown. To unveil the role of myotilin and αB-crystallin in the pathogenesis of MFM, we injected zebrafish fertilized eggs at one-cell stage with expression plasmids harboring cDNA sequences of human wildtype or mutated MYOT (p.Ser95Ile) and human wildtype or mutated CRYAB (p.Gly154Ser). We evaluated the effects on fish survival, motor behavior, muscle structure and development. We found that transgenic zebrafish showed morphological defects that were more severe in those overexpressing mutant genes which developed a myopathic phenotype consistent with that of human myofibrillar myopathy including the formation of protein aggregates. Results indicate that pathogenic mutations in myotilin and αB-crystallin genes associated with MFM cause a structural and functional impairment of the skeletal muscle in zebrafish, thereby making this non-mammalian organism a powerful model to dissect disease pathogenesis and find possible druggable targets

2D Discrete Mirror Transform for Image Non-Linear Approximation

In this paper, a new 2D transform named Discrete Mirror Transform (DMT) is presented. The DMT is computed by decomposing a signal into its even and odd parts around an optimal location in a given direction so that the signal energy is maximally split between the two components. After minimizing the information required to regenerate the original signal by removing redundant structures, the process is iterated leading the signal energy to distribute into a continuously smaller set of coefficients. The DMT can be displayed as a binary tree, where each node represents the single (even or odd) signal derived from the decomposition in the previous level. An optimized version of the DMT (ODMT) is also introduced, by exploiting the possibility to choose different directions at which performing the decomposition. Experimental simulations have been carried out in order to test the sparsity properties of the DMT and ODMT when applied on images: referring to both transforms, the results show a superior performance with respect to the popular Discrete Cosine Transform (DCT) and DiscreteWavelet Transform (DWT) in terms of non-linear approximation

Symmetry-Based Graph Fourier Transforms for Image Representation

It is well-known that the application of the Discrete Cosine Trans- form (DCT) in transform coding schemes is justified by the fact that it belongs to a family of transforms asymptotically equivalent to the Karhunen-Loe`ve Transform (KLT) of a first order Markov process. However, when the pixel-to-pixel correlation is low the DCT does not provide a compression performance comparable with the KLT. In this paper, we propose a set of symmetry-based Graph Fourier Transforms (GFT) whose associated graphs present a totally or par- tially symmetric grid. We show that this family of transforms well represents both natural images and residual signals outperforming the DCT in terms of energy compaction. We also investigate how to reduce the cardinality of the set of transforms through an analysis that studies the relation between efficient symmetry-based GFTs and the directional modes used in H.265 standard. Experimental results indicate that coding efficiency is high

The maximum cardinality of trifferent codes with lengths 5 and 6

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