From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree

In its most widespread imaging and vision applications, Ambrosio and Tortorelli (AT) phase field is a technical device for applying gradient descent to Mumford and Shah simultaneous segmentation and restoration functional or its extensions. As such, it forms a diffuse alternative to sharp interfaces or level sets and parametric techniques. The functionality of the AT field, however, is not limited to segmentation and restoration applications. We demonstrate the possibility of coding parts-features that are higher level than edges and boundaries-after incorporating higher level influences via distances and averages. The iteratively extracted parts using the level curves with double point singularities are organized as a proper binary tree. Inconsistencies due to non-generic configurations for level curves as well as due to visual changes such as occlusion are successfully handled once the tree is endowed with a probabilistic structure. As a proof of concept, we present (1) the most probable configurations from our randomized trees; and (2) correspondence matching results between illustrative shape pairs.


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There is a growing trend to design buildings with colourful and dynamic outer skins through the integration of digital media tools, particularly Led Emitting Diode (LED) systems, and the use of innovative technology. This integration has been discussed in recent conferences under the term “media façade” as a new research field. Discussing the intersection of media, technology, art, and architecture, this field introduces a new form of communication platform, urban space and public perception, which can be v...
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In this work, we make use of 3D contours and relations between them (namely, coplanarity, cocolority, distance and angle) for four different applications in the area of computer vision and vision-based robotics. Our multi-modal contour representation covers both geometric and appearance information. We show the potential of reasoning with global entities in the context of visual scene analysis for driver assistance, depth prediction, robotic grasping and grasp learning. We argue that, such 3D global reasoni...
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The success of deep learning in computer vision applications has led to the use of learning based algorithms also in image compression. Learning based lossless image compression algorithms can be divided into three categories, namely, pixel-by-pixel (or masked convolution based) algorithms, prior based algorithms and latent representation based algorithms. In the pixel-by-pixel algorithms, each pixel’s probability distribution is obtained by processing the previously coded left and upper neighbouring pixels...
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In this study, design and simulation of plasmonic nanoantenna structures to obtain high power enhancement capabilities at optical frequencies, as well as utilization of nanoantennas for imaging and sensing applications are presented. Plasmonic characteristics of nanoantennas, which depend on many parameters, such as material, frequency, geometry, and size, are investigated in detail via computational analyses of various nanoantenna structures. Numerical solutions of electromagnetic problems are performe...
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Multi-layer three-dimensional (3D) metamaterials have emerged as a platform to realize multifunctional chiral devices such as for asymmetric transmission. However, the alignment and fabrication methods of 3D chiral metamaterials are quite complex and time-consuming, which deteriorate the pragmatic use of such devices. Here, a unique type of direction-controlled single-layer metasurface hologram consisting of low loss hydrogenated amorphous silicon meta-atoms is proposed. The hologram behaves like a chiral m...
Citation Formats
Z. S. Tarı, “From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree,” JOURNAL OF MATHEMATICAL IMAGING AND VISION, pp. 69–86, 2014, Accessed: 00, 2020. [Online]. Available: