Blob parameter selection for image representation

Younes Benkarroum; Gabor T. Herman; Stuart W. Rowland

doi:10.1364/JOSAA.32.001898

Journal of the Optical Society of America A
Vol. 32,
Issue 10,
pp. 1898-1915
(2015)
•https://doi.org/10.1364/JOSAA.32.001898

Blob parameter selection for image representation

Younes Benkarroum, Gabor T. Herman, and Stuart W. Rowland

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Younes Benkarroum, Gabor T. Herman, and Stuart W. Rowland, "Blob parameter selection for image representation," J. Opt. Soc. Am. A 32, 1898-1915 (2015)

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Table of Contents Category
- Image Processing
Optics & Photonics Topics
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About this Article
History
- Original Manuscript: March 12, 2015
- Revised Manuscript: August 25, 2015
- Manuscript Accepted: September 2, 2015
- Published: September 30, 2015

Abstract

A technique for optimizing parameters for image representation using blob basis functions is presented and demonstrated. The exact choice of the basis functions significantly influences the quality of the image representation. It has been previously established that using spherically symmetric volume elements (blobs) as basis functions, instead of the more traditional voxels, yields superior representations of real objects, provided that the parameters that occur in the definition of the family of blobs are appropriately tuned. The technique presented in this paper makes use of an extra degree of freedom, which has been previously ignored, in the blob parameter space. The efficacy of the resulting parameters is illustrated.

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Equations (34)

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$j_{r}$	Root
$j_{1}$	6.987932
$j_{2}$	10.417119
$j_{3}$	13.698023
$j_{4}$	16.923621
$j_{5}$	20.121806
$j_{6}$	23.304247
$j_{7}$	26.476764
$j_{8}$	29.642605
$j_{9}$	32.803732

$j_{r_{1}}$ , $j_{r_{2}}$	$a$	$α$
$j_{1}$ , $j_{2}$	$1.738875 β$	3.294537
$j_{1}$ , $j_{3}$	$2.651778 β$	9.485434
$j_{1}$ , $j_{4}$	$3.469269 β$	13.738507
$j_{1}$ , $j_{5}$	$4.247117 β$	17.527826
$j_{1}$ , $j_{6}$	$5.003932 β$	21.105107
$j_{1}$ , $j_{7}$	$5.748062 β$	24.563319
$j_{1}$ , $j_{8}$	$6.483890 β$	27.946764
$j_{1}$ , $j_{9}$	$7.213964 β$	31.279745

$j_{r_{1}}$ , $j_{r_{2}}$	$q_{3} / q_{0}$	$q_{4} / q_{0}$	$q_{5} / q_{0}$
$j_{1}$ , $j_{2}$	$1.378761 \times 10^{- 3}$	$- 1.1.28555 \times 10^{- 3}$	$2.429460 \times 10^{- 5}$
$j_{1}$ , $j_{3}$	$2.030869 \times 10^{- 5}$	$- 1.095569 \times 10^{- 5}$	$6.241931 \times 10^{- 6}$
$j_{1}$ , $j_{4}$	$- 1.759383 \times 10^{- 7}$	$- 1.873667 \times 10^{- 7}$	$1.125839 \times 10^{- 7}$
$j_{1}$ , $j_{5}$	$- 1.011915 \times 10^{- 8}$	$- 3.034945 \times 10^{- 9}$	$2.024441 \times 10^{- 9}$
$j_{1}$ , $j_{6}$	$1.885230 \times 10^{- 10}$	$- 2.960094 \times 10^{- 12}$	$3.525051 \times 10^{- 11}$
$j_{1}$ , $j_{7}$	$8.038446 \times 10^{- 12}$	$2.974920 \times 10^{- 12}$	$4.761025 \times 10^{- 13}$
$j_{1}$ , $j_{8}$	$- 3.048963 \times 10^{- 13}$	$1.672062 \times 10^{- 13}$	$- 2.001146 \times 10^{- 15}$
$j_{1}$ , $j_{9}$	$- 5.836311 \times 10^{- 15}$	$5.456460 \times 10^{- 15}$	$- 5.990216 \times 10^{- 16}$

$r_{1} \ r_{2}$	2	3	4	5	6	7	8	9
1	0.47367	0.24554	0.23447	0.26334	0.29724	0.32804	0.35421	0.37599
2			0.23470	0.26398	0.29721	0.32778	0.35393	0.37574
3				0.31407	0.30922	0.33244	0.35601	0.37675
4						0.36309	0.36702	0.38176
5							0.42496	0.40043

$θ$	$(r_{1}, r_{2})$	$E_{β, θ, r_{1}, r_{2}}$	$E_{β, θ, STD}$
¼	(1,2)	0.10354	0.16390
1	(1,3)	0.17054	0.17817
2	(1,3)	0.19554	0.19719
4	(1,4)	0.23447	0.23524
8	(2,4)	0.25586	0.31133

	Voxels	Standard Blobs $α = 10.4$	Standard Blobs $α = 10.444256$	Recommended Blobs
Abdomen	0.221928	0.066382	0.066458	0.063463
Thorax	0.220511	0.079533	0.079568	0.080059

Abstract

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Tables (6)

Equations (34)

Journal of the Optical Society of America A