30th November 2009

ROI-based procedures for progressive transmission of digital images: A comparison

Published paper “ROI-based procedures for progressive transmission of digital images: A comparison” (I. Baeza, J.A. Verdoy, J. Villanueva-Oller, R.J. Villanueva), in the Mathematical and Computer Modelling nº 50, ISSN 0895-7177, pp. 849-859 (year 2009).

Nowadays, problems arise when handling big-sized images (i.e. medical image such as Computed Tomographies or satellite images) of 10, 50, 100 or more Megabytes, due to the amount of time required for transmiting and displaying, being this time even worse when a narrow bandwidth transmission media is involved (i.e. dial-up or mobile network), because receiver must wait until the entire image has arrived. To solve this issue, progressive transmission schemes are used. These schemes allow image sender to enconde the image data in such a way that it is possible for the receiver to perform a reconstruction of the original image since the very beginning of transmission. Despite this reconstruction being, of course, partial, it is possible to improve the reconstruction on the fly, as more and more information of the original image is received. There are many progressive transmission methods available, such as bit planes, TSVQ, DPCM, and, more recently, matrix polynomial interpolation, Discrete Cosine Transform (DCT, used in JPEG) and wavelets (used in JPEG2000). However, none of them are well suited, or perform poorly, when, in addition to progressive transmission, we want to include also ROIs (Region Of Interest) handling. In progressive transmission of ROIs, we want not only yo reconstruct the image as we receive image data, but also be able to select which part or parts of the emerging image we think are relevant and want to receive first, and which part or parts have no interest. In this context we present an algorithm for lossy adaptive encoding based on regular value decomposition (SVD). This algorithm turns out to be well suited for progressive transmission and ROI selection of 2D and 3D images, as it is able to avoid redundancy in data transmission and does not require any sort of data recodification, even if we select arbitrary ROIs on the fly.

Keywords: Adaptive progressive transmission, ROI, Region of Interest, reconstruction, singular value decomposition.

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18th October 2008

A comparison of ROI-based procedures for progressive transmission of digital images

Published book chapter “A comparison of ROI-based procedures for progressive transmission of digital images” (I. Baeza, J.A. Verdoy, J. Villanueva-Oller, R.J. Villanueva), Modelling for Engineering and Medicine 2008, ISBN 978-84-691-8345-8, pp. 146-161 (year 2008). Ed. Instituto de Matemática Multidisciplinar.

In this paper we review and compare several progressive transmission schemes capable of Region Of Interest (ROI) handling:

– Discrete Cosine Transform / JPEG
– Wavelets / JPEG2000
– Singular Value Decomposition

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13th September 2008

ROI-based procedures for progressive transmission of digital images: A comparison

Presented conference “ROI-based procedures for progressive transmission of digital images: A comparison” (I. Baeza, C. Mora, J.A. Verdoy, J. Villanueva Oller) in the congress

X Jornadas de Investigación y Fomento de la Multidisciplinariedad
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia.
X JIFM, Valencia, España, 9-12/09/2008.

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15th October 2007

Cálculo exacto de una matriz de pesos para un aparato TAC de fan-beam. Reconstrucciones ART mediante el algoritmo de Kaczmarz

Published book chapter “Cálculo exacto de una matriz de pesos para un aparato TAC de fan-beam. Reconstrucciones ART mediante el algoritmo de Kaczmarz” (M.J. Rodríguez Álvarez, R.J. Villanueva, J. Villanueva-Oller), in the Anales de Ingeniería Técnica Informática de Sistemas nº 1, ISBN 978-84-935511-2-4, pp. 119-164 (año 2007). Ed. Felipe II Libros.

Abstract not available in English

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14th May 2007

CASANDRA: A prototype implementation of a system of network progressive transmission of medical digital images

Published paper “CASANDRA: A prototype implementation of a system of network progressive transmission of medical digital images” (J. Villanueva-Oller, R.J. Villanueva, S. Díez), in the Computer Methods and Programs in Biomedicine nº 85, ISSN 0169-2607, pp. 152-164, (year 2007). Ed. Elsevier Ireland.

In this paper, a prototype for progressive transmission of medical digital 2D images through the network, called CASANDRA, is presented. The prototype consists of the server part and the client part. In the server part, the images are acquired, stored, computed their wavelet transform and the wavelet coefficients stored, then transmitted progressively, when required, via TCP to the client. In the client part, with the inverse wavelet ransform, the received wavelet coefficients are used to build successive improved reconstructions of the image. This prototype has been implemented and is being tested in the Radiotherapy Service of the Valencia University Hospital (Valencia, Spain).

Keywords Medical images, Network progressive transmission, Radio-diagnostic

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30th July 2004

Progressive imaging: S-transform order

Published paper “Progressive imaging: S-transform order” (H. Zhu, R.A. Brown, R.J. Villanueva, J. Villanueva Oller, M.L. Lauzon, J.R. Mitchell, A.G. Law), in the Australian & New Zealand Industrial and Applied Mathematics Journal (ANZIAM J), vol. 45 (E), ISSN 1446-1811, pp. C1002-1016 (year 2004). Ed. Australian Mathematical Society.

The paper focuses on progressive transmission of CT or MR images, and introduces two general schemes that are built around information embedded in transforms of images. A direct, a priori ordering of 93, parallel, CT slices of a head is obtained by successively finer sweepings of their natural subscript ordering to give a benchmark illustration. By comparison, an ordering of these CT slices simply by their energies is seen to not provide a viable progressive imaging scheme, at least when an overall, 3D skin level rendering is the gauge employed. To investigate progressive imaging that does not obscure internal detail, two techniques based on transform space information are introduced here, and illustrated in detail with a 128 × 128 MR slice of a head I(x, y). The first uses decreasing size of the moduli of the elements of the Fourier transform F(kx, ky) of I(x, y). The second, a one parameter generalization, exploits the localization feature of the recent S-transform and also provides a capability for an observer to outline a region of interest within the progressive transmission process. Both transform based methods are effective for the specific illustrations included, and the latter opens important research questions for application in analysis, handling or interpretation of the massive data sets arising in magnetic resonance imaging.

Keywords: S-transform, progressive transmission, interpolation, Fourier transform.

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6th May 2004

Progressive Imaging: a Transform Space Approach

Presented conference “Progressive Imaging: a Transform Space Approach” (Robert A. Brown, Javier Villanueva Oller) in the

SIAM Conference on Imaging Science 2004
SIAM Activity Group on Imaging Science (SIAG/IS) (Sponsor)
Marriot Coty Center, Salt Lake City, Utah, EEUU, 3-5/05/2004.

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12th July 2003

Progressive transmission of MR images, through energy-ordering in S-transform space

Presented conference “Progressive transmission of MR images, through energy-ordering in S-transform space” (H. Zhu, R.A. Brown, R..J. Villanueva, J. Villanueva Oller, M.L. Lauzon, J.R. Mitchell, A.G. Law) in the

5th International Congress on Industrial and Applied Mathematics
Ross. R. Moore (Editor),
ICIAM, Sydney, Australia, 7-11/07/2003.

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30th July 2002

Matrix Cubic Splines for Progressive 3D Imaging

Published paper “Matrix Cubic Splines for Progressive 3D Imaging” (E. Defez, J. Villanueva Oller, R.J. Villanueva), in the Journal of Mathematical Imaging and Vision, nº 17, ISSN 0924-9907, pp. 41-53 (year 2002). Ed. Springer.

Mathematical theory of matrix cubic splines is introduced, then adapted for progressive rendering of images. 2D subsets of a 3D digital object are transmitted progressively under some rendering scheme, and subsequent reconstructions using the matrix cubic spline algorithm provide an evolving 3D rendering. The process can be an effective tool for browsing three dimensional objects, and effectiveness is illustrated with a test data set consisting of 93 CT slices of a human head. The procedure has been implemented on a single processor PC system, to provide a platform for full 3D experimentation; performance is discussed. A web address for the complete, documented Mathematica code is given.

Keywords: progressive 3D rendering, progressive transmission of images, matrix cubic splines, matrix polynomial reconstructions.

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30th May 2002

Matrix Newton interpolation and progressive 3D imaging: PC-based computation

Published paper “Matrix Newton interpolation and progressive 3D imaging: PC-based computation” (E. Defez, A. Law, J. Villanueva Oller, R.J. Villanueva), in the Mathematical And Computer Modelling, nº 35, ISSN 0895-7177, pp. 303-322 (year 2002). Ed. Pergamon-Elsevier.

For polynomials P(x) = Anxn + An-1xn-1 + … + A1x + A0 in a real scalar x, but with coefficients Aj that are rectangular matrices, a generalization of Newton’s divided difference interpolatory scheme is developed. Instances of P(x) at nodes xi may be interpreted as slices of a digital 3D object. Mathematica code for this machinery is given and its effectiveness illustrated for progressively-transmitted renderings. Analysis, with supporting Mathematica code, is extended to a piecewise matrix polynomial situation, to produce practicable software for a PC-based performance evaluation. How a 3D object is decomposed into 2D subsets in preparation for progressive transmission, as well as their selected ordering for transmission, are seen to affect quality of the emerging reconstructions. Extension to 4D objects is also discussed briefly, to provide introduction to, for example, application of matrix polynomial machinery within the field of functional magnetic resonance imaging.

Keywords: progressive transmission of images, matrix Newton interpolation, matrix polynomial reconstruction, PC-based progressive rendering.

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30th April 2000

Progressive transmission of images: PC-based computations using orthogonal matrix polynomials

Published paper “Progressive Transmission of Images: PC-Based Computations, Using Orthogonal Matrix Polynomials” (E. Defez, A. Law, J. Villanueva Oller, R.J. Villanueva) in the Mathematical And Computer Modelling, nº 32, ISSN 0895-7177, pp. 1125-1140 (year 2000).

Two methods for reconstructing a 3-D image as its 2-D parallel slices are transmitted progressively, in some order, are presented and analyzed. In the originating data base, an ordered set of 2-D slices could represent computer tomography (CT), magnetic resonance images (MRI) or cryosection cross-sections of a 3-D object, for example. With this digital formulation, matrix interpolation machinery renders a progressively-improving image as slices are received. A piecewise matrix polynomial reconstruction is also considered for reducing computational needs.

Keywords: Progressive transmission of images, Matrix orthogonal polynomials, Piecewise matrix polynomials interpolation, Matrix polynomial reconstruction, Rendering.

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