Computational Geometry, Topology and Physics of Visual Scenes

Peters, James F.

doi:10.1007/978-3-030-22192-8_1

Cited by 3 publications

(2 citation statements)

References 35 publications

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“…, (N/2) and k q p,3 (u) = E y q p−1,1,s (u), y q p−1,2,s (u) . For the level p = 1 only, the relations (22) and (23) are transformed as follows:…”

Section: Adaptive Control For Each Level Of Fo-ahkltmentioning

confidence: 99%

“…The future investigations of 3D FO-AHKLT and 3D-AFWHT will be aimed at the evaluation of their characteristics compared to famous tensor decompositions, in order to define the best settings and to define the most efficient applications for tensor image compression, feature space reduction, filtration, analysis, search and recognition of multidimensional visual information, deep learning, etc. The future development of the presented algorithm will be aimed at applications related to tree tensor network [20], multiway array (tensor) data analysis [21,22], tensor decompositions in neural networks for tree-structured data, etc.…”

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confidence: 99%

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Third-Order Tensor Decorrelation Based on 3D FO-HKLT with Adaptive Directional Vectorization

Kountchev

Mironov

Kountcheva³

2022

Symmetry

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In this work, we present a new hierarchical decomposition aimed at the decorrelation of a cubical tensor of size 2n, based on the 3D Frequency-Ordered Hierarchical KLT (3D FO-HKLT). The decomposition is executed in three consecutive stages. In the first stage, after adaptive directional vectorization (ADV) of the input tensor, the vectors are processed through one-dimensional FO-Adaptive HKLT (FO-AHKLT), and after folding, the first intermediate tensor is calculated. In the second stage, on the vectors obtained after ADV of the first intermediate tensor, FO-AHKLT is applied, and after folding, the second intermediate tensor is calculated. In the third stage, on the vectors obtained from the second intermediate tensor, ADV is applied, followed by FO-AHKLT, and the output tensor is obtained. The orientation of the vectors, calculated from each tensor, could be horizontal, vertical or lateral. The best orientation is chosen through analysis of their covariance matrix, based on its symmetry properties. The kernel of FO-AHKLT is the optimal decorrelating KLT with a matrix of size 2 × 2. To achieve higher decorrelation of the decomposition components, the direction of the vectors obtained after unfolding of the input tensor in each of the three consecutive stages, is chosen adaptively. The achieved lower computational complexity of FO-AHKLT is compared with that of the Hierarchical Tucker and Tensor Train decompositions.

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“…, (N/2) and k q p,3 (u) = E y q p−1,1,s (u), y q p−1,2,s (u) . For the level p = 1 only, the relations (22) and (23) are transformed as follows:…”

Section: Adaptive Control For Each Level Of Fo-ahkltmentioning

confidence: 99%

mentioning

confidence: 99%

Third-Order Tensor Decorrelation Based on 3D FO-HKLT with Adaptive Directional Vectorization

Kountchev

Mironov

Kountcheva³

2022

Symmetry

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Advances in Bessel image sharpness analysis

Don

Peters

2021

Math Methods in App Sciences

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This paper introduces advances in the use of Bessel functions (cylinder functions) in achieving optimal sharpness of shapes delineated by collections of holes (dark valley regions) and bright regions in different areas of a video frame in terms of 4D voxels (grayscale video frame picture elements with coordinates (x, y, g, t) at location x, y with intensity g, and elapsed time t). An image hole is an island of low voxel intensities surrounded by varying voxel intensity peaks. The basic approach is to identify dominant collections of lights (high voxel intensity peaks) and darks (low voxel intensity clusters) in video frames. A main finding in this paper is that surface objects (recorded in images) are sharper wherever there are preponderant contrasting differences between image lights and darks. These contrasting differences lead to the highly accurate detection of shape holes (dark valleys) that delineate surface shapes recorded in sequences of video frames. With the use of cylindrical Bessel functions introduced by F. W. Bessel in 1824, contrasting differences between peaks and valleys can be measured in terms of voxel intensities and voxel indices.

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