Diego Santa-Cruz

MESH: measuring errors between surfaces using the Hausdorff distance

This paper proposes an efficient method to estimate the distance between discrete 3D surfaces represented by triangular 3D meshes. The metric used is based on an approximation of the Hausdorff distance, which has been appropriately implemented in order to reduce unnecessary computation and memory usage. Results show that when compared to similar tools, a significant gain in both memory and speed can be achieved.

JPEG 2000 performance evaluation and assessment

Abstract JPEG 2000, the new ISO/ITU-T standard for still image coding, has recently reached the International Standard (IS) status. Other new standards have been recently introduced, namely JPEG-LS and MPEG-4 VTC. This paper provides a comparison of JPEG 2000 with JPEG-LS and MPEG-4 VTC, in addition to older but widely used solutions, such as JPEG and PNG, and well established algorithms, such as SPIHT. Lossless compression efficiency, fixed and progressive lossy rate-distortion performance, as well as complexity and robustness to transmission errors, are evaluated. Region of Interest coding is also discussed and its behavior evaluated. Finally, the set of provided functionalities of each standard is also evaluated. In addition, the principles behind each algorithm are briefly described. The results show that the choice of the “best” standard depends strongly on the application at hand, but that JPEG 2000 supports the widest set of features among the evaluated standards, while providing superior rate-distortion performance in most cases.

JPEG 2000 still image coding versus other standards

JPEG 2000, the new ISO/ITU-T standard for still image coding, is about to be finished. Other new standards have been recently introduced, namely JPEG-LS and MPEG-4 VTC. This paper puts into perspective the performance of these by evaluating JPEG 2000 versus JPEG-LS and MPEG-4 VTC, as well as the older but widely used JPEG. The study concentrates on compression efficiency, although complexity and set of supported functionalities are also evaluated. Lossless compression efficiency as well as the lossy rate-distortion behavior is discussed. The principles behind each algorithm are briefly described and an outlook on the future of image coding is given. The results show that the choice of the “best” standard depends strongly on the application at hand.

An analytical study of JPEG 2000 functionalities

JPEG 2000, the new ISO/ITU-T standard for still image coding, is about to be finished. Other new standards have been recently introduced, namely JPEG-LS and MPEG-4 VTC. This paper compares the set of features offered by JPEG 2000, and how well they are fulfilled, versus JPEG-LS and MPEG-4 VTC, as well as the older but widely used JPEG and the PNG. The study concentrates on the set of supported features, although lossless and lossy progressive compression efficiency results are also reported. Each standard, and the principles of the algorithms behind them, are also described. As the results show, JPEG 2000 supports the widest set of features among the evaluated standards, while providing superior rate-distortion performance.

New approach to JPEG 2000 compliant Region Of Interest coding

Region Of Interest (ROI) coding is one of the innovative functionalities supported by JPEG 2000, the new ISO/ITU-T still image coding standard developed by the Joint Photographic Experts Group (JPEG). It enables a non-uniform distribution of the image quality between a selected region (the ROI) and the rest of the image (background). This feature is obtained by scaling background coefficients in the wavelet domain. According to the ROI Maxshift method defined in JPEG 2000 part 1 (baseline algorithm), the background bit-planes are down-shifted below all ROI coefficients. In addition, the ROI can have any shape as the latter does not need to be transmitted to a JPEG 2000 decoder (no codestream overhead due to the coding of the shape). On the contrary, this method requires decoding of all ROI coefficients before accessing bit-planes of the background. Furthermore, it uses large shifting values that significantly increase the number of total bit-planes to encode. In JPEG 2000 part 2 (extensions), a generic (Scaling based) ROI coding has been included. This method supports any scaling values. In particular, it allows a rough control on both ROI and background qualities distributions in the codestream, but implies the derivation of a ROI bit-mask at the decoding side. This paper starts by providing some hints on how to choose an optimal Maxshift scaling value, as well as how to pad the ROI extra bits appearing during the shift operation. Then, it proposes an encoding algorithm that combines advantages of both ROI methods. This algorithm can be used by applications where visually lossless ROI*s is acceptable and is based on an extension of the Maxshift method to low scaling values. The generated codestreams remain compliant with the Maxshift decoding algorithm described in JPEG 2000 part 1, and can be consequently handled by any JPEG 2000 decoder.

Opening the Laplacian pyramid for video coding

Laplacian pyramids are used in the framework of scalable video coding to efficiently provide spatial scalability. In literature, closed-loop schemes are adopted to implement such codecs. Closed-loop introduces complexity and optimization drawbacks. In this paper we investigate mechanisms to provide an open loop version of the Laplacian pyramid. We call our approach the Laplacian pyramid with update (LPU). In this scheme, different filter-banks can be used: we propose an intuitive framework to design filters that provides efficient video coding. The interesting result of this work is that LPU enables coding performances at least equivalent to those reported for closed loop Laplacian pyramids with advantages both in terms of complexity, rate-distortion optimization and independence of the qualities of the different resolutions.

Coding of 3D virtual objects with NURBS

With the advancement of computer graphics in the recent years, an increasing number of pictures, video and 3D content is generated by synthesis processing rather than acquired with capture devices such as cameras or scanners. Several techniques have been developed for compression of discrete (i.e. piece-wise planar) 3D models, in the form of 3D polygonal meshes. However, no important attempt has been made to compress the smooth surfaces of artificially generated 3D models, that are most often represented as parametric surfaces, of which Non-Uniform Rational B-Spline (NURBS) is a popular form. This paper presents a method for compressing NURBS 3D models with a small and controllable loss. The scheme uses a differential pulse coded modulation coder with different predictors for knot values and control points, coupled with a uniform scalar quantizer, followed by a bitplane arithmetic entropy coder. The multiplicity of knots is preserved by the use of a multiplicity map. The rate-distortion characteristics of the proposed scheme are evaluated on various models. When compared to MPEG-4 (ISO/IEC 14496-2:1999: information technology--coding of andio-visual objects--Part 2: Visual, December 1999; ISO/IEC 14496-2:1999/Amd 1:2000: visual extensions, August 2000) and Touma-Gotsman (Proceedings of the 24th Conference on Graphics Interface (GI-98), Morgan Kaufmann, Los Altos, CA, San Francisco, CA, June 1998, pp. 26-34) compressed triangular meshes, the proposed scheme achieves more than five times better compression, for equivalent L2 error and much better visual quality.

Compression of parametric surfaces for efficient 3D model coding

In the field of compression, the type of 3D models traditionally considered is that of polygonal meshes, for which several efficient compression techniques have been proposed in the recent years. Nowadays, an increasing proportion of 3D models are created by a synthesis or modeling process, instead of captured from the real world. Such models are most often given as parametric surfaces, which have several advantages over polygonal meshes, such as resolution independence and a more compact representation. This paper proposes a method to code parametric surfaces, given as Non-Uniform Rational B-Splines (NURBS). The coding scheme consists in coding the NURBS parameters (knots and control points) using a predictive scheme, coupled with uniform quantization and entropy coding. The multiplicity of knots is preserved by decomposing the knot vectors in a break vector (the values) and a multiplicity map. The rate-distortion of the proposed scheme is evaluated and compared against compressed triangular meshes. The results show that a considerable compression ratio is achievable under visually lossless conditions, that outperforms by far triangular meshes. In addition of having a better rate-distortion performance, the coding scheme enables the efficient transmission of synthesized 3D models retaining their resolution independence.