Octahedral Transforms for 3-D Image Processing

Lenz, Reiner; Carmona, Pedro

doi:10.1109/tip.2009.2029953

Cited by 4 publications

(3 citation statements)

References 18 publications

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“…In grouplets, the wavelet coefficients are grouped together based on the direction of their flow using multiscale association fields. Representation theory using rotations and reflections have been used by Lenz [13,14] for edge detection in images but they do not generalize the use of transformation groups to generate an orthogonal basis. In a recent work by Lenz, octahedral transformation group has been chosen to be suitable for a specific application, i.e., the 3-D image environment, and representations have been used to describe this environment by evaluating their correlation coefficients.…”

Section: Transformationsmentioning

confidence: 99%

On Finite Group Presentations and Function Decomposition Based on Linearity of Discrete-Time Signal

Ngulde

Madu

Samaila

2018

ARJOM

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Based on the concept of group representation theory, new representations can be generated by direct product (or tensor product) of any two representations of a group. In such case, their irreducible representations are also the direct product. But the conditions under which these representations can be chosen and how to decompose them is silent. In this work, a clear and efficient method for generating and decomposing representations is presented. The study is restricted to geometric group D n of order 2n and its subgroups, where a new homomorphism called a transfer function based on the geometric group is constructed. Due to linearity of discrete-time signal, the generated transformations are used on signal space. Thus, a different approach to signal processing with the choice of a group of transformations is established.

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Section: Transformationsmentioning

confidence: 99%

On Finite Group Presentations and Function Decomposition Based on Linearity of Discrete-Time Signal

Ngulde

Madu

Samaila

2018

ARJOM

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“…In comparison with traditional two-dimensional (2-D) fingerprint images, plentiful fingerprint information can be retrieved from the 3-D fingerprint models, thus making the subsequent fingerprint recognition more reliable. 3 Compared with the traditional 2-D image-based fingerprinting techniques, 3-D fingerprinting is still a new research domain that appears in recent years. The major technical challenge involved in 3-D fingerprinting is how to capture the 3-D model of live fingerprint precisely and efficiently.…”

Section: Introductionmentioning

confidence: 99%

Real-time three-dimensional fingerprint acquisition via a new photometric stereo means

2013

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Abstract. A real-time means for three-dimensional (3-D) fingerprint acquisition is presented. The system is configured with only one camera and some white light-emitting diode lamps. The reconstruction is performed based on the principle of photometric stereo. In the algorithm, a two-layer Hanrahan-Krueger model is proposed to represent the finger surface reflectance property instead of the traditional Lambert model. By the proposed lighting direction calibration and the nonuniform lighting correction methods, surface normal at each image point can be accurately estimated by solving a nonlinear optimization problem. Finally, a linear normal transformation is implemented for the enhancement of 3-D models. The experiments are implemented with real finger and palm prints, and the results are also compared with traditional means to show its feasibility and improvement in the reconstruction accuracy. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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“…In grouplets, the wavelet coefficients are grouped together based on the direction of their flow using multiscale association fields. Representation theory using rotations and reflections have been used by Lenz [17] [18] for edge detection in images but they do not generalize the use of transformation groups to generate an orthogonal basis. In a recent work by Lenz, octahedral transformation group has been chosen to be suitable for a specific application, i.e., the 3-D image environment, and representations have been used to describe this environment by evaluating their correlation coefficients.…”

Section: Introductionmentioning

confidence: 99%

G-Lets: A New Signal Processing Algorithm

Rajathilagam¹,

Rangarajan²,

Soman³

2012

IJCA

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Different signal processing transforms provide us with unique decomposition capabilities. Instead of using specific transformation for every type of signal, we propose in this paper a novel way of signal processing using a group of transformations within the limits of Group theory. For different types of signal different transformation combinations can be chosen. It is found that it is possible to process a signal at multiresolution and extend it to perform edge detection, denoising, face recognition, etc by filtering the local features. For a finite signal there should be a natural existence of basis in it's vector space. Without any approximation using Group theory it is seen that one can get close to this finite basis from different viewpoints. Dihedral groups have been demonstrated for this purpose. General Termssignal processing, algorithm, group theory.

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Octahedral Transforms for 3-D Image Processing

Cited by 4 publications

References 18 publications

On Finite Group Presentations and Function Decomposition Based on Linearity of Discrete-Time Signal

On Finite Group Presentations and Function Decomposition Based on Linearity of Discrete-Time Signal

Real-time three-dimensional fingerprint acquisition via a new photometric stereo means

G-Lets: A New Signal Processing Algorithm

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