Fast and accurate algorithm for 3D local object reconstruction using Krawtchouk moments

Mesbah, Abderrahim; Mallahi, Mostafa El; Lakhili, Zouhir; Qjidaa, Hassan; Berrahou, Aissam

doi:10.1109/icmcs.2016.7905559

Cited by 9 publications

(5 citation statements)

References 17 publications

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“…Figure 1 shows the 3D plot of the Tchebichef polynomial values using Algorithm 1, where the horizontal axis represents the Tchebichef polynomials in terms of the parameter x. In contrast, the vertical axis represents the values in terms [20,21,25,[27][28][29] Matrix Product O n…”

Section: Tchebichef Polynomialsmentioning

confidence: 99%

“…Among the most outstanding works is Hosny et al [19], which presents an algorithm for calculating Legendre moments, using parallel multicore processors and GPUs. Mesbah et al [20,21], uses a fast and accurate algorithm based on matrix multiplication to extract local characteristics of 3D Krawtchouk moments. Karmouni et al presents the fast and stable computation of Mexnier [22] and Charlier [23] 3D moments by using digital filters the Z transformation and dividing it into a set of fixed-size blocks that are processed moments separately.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, Sayyouri et al [25] performs a way to compute generalized Laguerre orthogonal polynomials based on matrix multiplication. From the previous works, there are three strategies for moment computation; direct calculation, dividing the object into cubes [18,[22][23][24]26] and calculating using matrices [20,21,25,[27][28][29].…”

Section: Introductionmentioning

confidence: 99%

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Fast computation of 3D Tchebichef moments for higher orders

Rivera-López

Camacho-Bello

Vargas-Vargas

et al. 2021

J Real-Time Image Proc

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This article proposes a new method for the fast and efficient calculation of 3D Tchebichef moments,which are an essential tool for the characterization and analysis of 3D objects. This method integrates the Kronecker tensor product to the computation of 3D Tchebichef moments for higher orders with the advantage of being parallelizable. The experimental results clearly show the benefits and efficacy of the proposed method compared to existing methods. Keywords 3D discrete orthogonal Tchebichef moments • Fast computation • 3D image reconstruction • High-order moments • Kronecker tensor product

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Section: Tchebichef Polynomialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fast computation of 3D Tchebichef moments for higher orders

Rivera-López

Camacho-Bello

Vargas-Vargas

et al. 2021

J Real-Time Image Proc

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show abstract

“…According to performance, 3D Krawtchouk moments have been proposed for content-based search and retrieval in [11]. Others have carefully examined their accuracy and efficiency on 3D object analysis and recognition [12]. Recent research [13] on protein local surface shape comparison first employed 3D Krawtchouk moments on irregular shapes instead of well-known 3D shape database.…”

Section: Moment Based Shape Featuresmentioning

confidence: 99%

Towards Understanding Speciation By Automated Extraction And Description Of 3d Foraminifera Stacks

Zhang

Ezard

Searle-Barnes

et al. 2020

2020 IEEE Southwest Symposium on Image Analysis and Interpretation (SSIAI)

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The sheer volume of 3D data restricts understanding of genetic speciation when analyzing specimens of planktonic foraminifera and so we develop an end-to-end computer vision system to solve and extend this. The observed fossils are planktonic foraminifera, which are single-celled organisms that live in vast numbers in the world's oceans. Each foram retains a complete record of its size and shape at each stage along its journey through life. In this study, a variety of individual foraminifera are analyzed to study the differences among them and compared with manually labelled ground truth. This is an approach which (i) automatically reconstructs individual chambers for each specimen from image sequences, (ii) uses a shape signature to describe different types of species. The automated analysis by computer vision gives insight that was hitherto unavailable in biological analysis: analyzing shape implies understanding spatial arrangement and this is new to the biological analysis of these specimens. By processing datasets of 3D samples containing 9GB of points, we show that speciation can indeed now be analyzed and that automated analysis from morphological features leads to new insight into the origins of life.

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“…Despite the compact representation and discriminative powers of these moments, the theory of invariants based on 3D Krawtchouk polynomials has not been well studied. Also, the very critical local retrieval property of the 3D moments has been noticed in [20], but much of the focus is given to their fast computation. We propose a new approach on this long-standing issue of local image comparison by constructing 3D Krawtchouk descriptors (3DKD) for describing local 3D surfaces.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional Krawtchouk descriptors for protein local surface shape comparison

Sit

Shin

2019

Pattern Recognition

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Direct comparison of three-dimensional (3D) objects is computationally expensive due to the need for translation, rotation, and scaling of the objects to evaluate their similarity. In applications of 3D object comparison, often identifying specific local regions of objects is of particular interest. We have recently developed a set of 2D moment invariants based on discrete orthogonal Krawtchouk polynomials for comparison of local image patches. In this work, we extend them to 3D and construct 3D Krawtchouk descriptors (3DKD) that are invariant under translation, rotation, and scaling. The new descriptors have the ability to extract local features of a 3D surface from any region-of-interest. This property enables comparison of two arbitrary local surface regions from different 3D objects. We present the new formulation of 3DKD and apply it to the local shape comparison of protein surfaces in order to predict ligand molecules that bind to query proteins. from them do not carry any error due to discretization unlike many other moments related to continuous functions [23]. 2) These polynomials are orthogonal; each moment brings in a new feature of the image, where minimum redundancy is critical in their discriminative performance. Moreover, they are directly defined in the image coordinate space, and hence their orthogonality property is well retained in the computed moments. 3) They are complete with a finite number of functions (equal to the image size) while many other polynomial spaces have infinitely many members. 4) They have the ability to retrieve local image patches by only changing the resolution of reconstruction and using low order moments. 5) The location of the patch can also be controlled by changing three parameters and hence shifting the region-of-interest along each dimension. 6) We also prove that these moments can be transformed into local descriptors, which are invariant under translation, rotation, and scaling. Therefore, using only a small number of invariant descriptors per image will make it possible to develop an efficient method for quick local image retrieval.Moment-based approaches, particularly Krawtchouk moments, are very useful for representing biological and medical images as they are pixelized or voxelized data. In medical imaging, such as computerized tomography (CT) scan and magnetic resonance imaging (MRI), objects are observed at different viewpoints and local images need to be extracted and examined. In digital pathology, for instance, pathologists are interested in information about specific structures rather than the whole image [9]. Thus, it is necessary to construct moment invariants that do not change by translation, rotation, and scaling and can retrieve local image patches or subimages.

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Fast and accurate algorithm for 3D local object reconstruction using Krawtchouk moments

Cited by 9 publications

References 17 publications

Fast computation of 3D Tchebichef moments for higher orders

Fast computation of 3D Tchebichef moments for higher orders

Towards Understanding Speciation By Automated Extraction And Description Of 3d Foraminifera Stacks

Three-dimensional Krawtchouk descriptors for protein local surface shape comparison

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