A mesh-generation framework for image representation based on data-dependent triangulation is proposed. The proposed framework is a modified version of the frameworks of Rippa and Garland and Heckbert that facilitates the development of more effective mesh-generation methods. As the proposed framework has several free parameters, the effects of different choices of these parameters on mesh quality are studied, leading to the recommendation of a particular set of choices for these parameters. A mesh-generation method is then introduced that employs the proposed framework with these best parameter choices. This method is demonstrated to produce meshes of higher quality (both in terms of squared error and subjectively) than those generated by several competing approaches, at a relatively modest computational and memory cost.

A flexible new mesh-generation framework for image representation is proposed, based on Delaunay triangulations. It is shown that this framework can be used to form a postprocessing optimization step that, when added to other previously-proposed methods, yields meshes of much greater quality. A new mesh-generation method, called IDDT, is also derived using the proposed framework, and shown to yield meshes of much better quality than those produced by previously-proposed methods as well as optimized versions of these methods constructed with the proposed framework.

Based on the greedy-point removal (GPR) scheme of Demaret and Iske, a simple yet highly effective framework for constructing triangle-mesh representations of images, called GPRFS, is proposed. By using this framework and ideas from the error diffusion (ED) scheme (for mesh-generation) of Yang et al., a highly effective mesh-generation method, called GPRFS-ED, is derived and presented. Since the ED scheme plays a crucial role in our work, factors affecting the performance of this scheme are also studied in detail. Through experimental results, our GPRFS-ED method is shown to be capable of generating meshes of quality comparable to, and in many cases better than, the state-of-the-art GPR scheme, while requiring substantially less computation and memory. Furthermore, with our GPRFS-ED method, one can easily trade off between mesh quality and computational/memory complexity. A reduced-complexity version of the GPRFS-ED method (called GPRFS-MED) is also introduced to further demonstrate the computational/memory-complexity scalability of our GPRFS-ED method.

A new content-adaptive mesh-generation method for image representation, based on the greedy point-removal scheme of Demaret and Iske, is proposed. The proposed method is shown to be capable of producing meshes of higher quality than those generated by the scheme of Demaret and Iske, while requiring substantially less computation and memory. Furthermore, with the proposed method, one can easily tradeoff between mesh quality and computational/memory complexity as needed. Since a mesh-generation scheme proposed by Yang et al. is a key component of the proposed method, some factors affecting the performance of this scheme are also explored.

In earlier work, Demaret and Iske proposed the scattered data coding (SDC) method for (single-rate) coding of arbitrarily-sampled image data. In this paper, several modifications to the SDC method are proposed in order to remove some limitations of the original scheme, improve coding efficiency, and add a progressive lossy-to-lossless coding capability. Through experimental results, the proposed method is shown to yield a significant improvement in coding efficiency (relative to the original SDC method) as well as provide an efficient progressive lossy-to-lossless coding capability.

A simple image coder based on triangle meshes is proposed, and several mesh-generation methods are presented, some previously proposed and some new. Then, our coder is used to evaluate the performance of the various mesh-generation methods. One of our proposed mesh-generation schemes, inspired by the work of Garland and Heckbert, is shown to perform best. The performance of linear and Clough-Tocher interpolation is also compared. Linear interpolation is found to perform better than Clough-Tocher interpolation, with the latter performing more poorly largely due to overshoot/undershoot near image edges.

It has been observed that filter banks from a certain popular separable 2D wavelet class always appear to have a higher coding gain with respect to a separable image model than with respect to an isotropic one. This behavior is examined in detail and an explanation for it is offered. As it turns out, for such filter banks, it is highly improbable (if not impossible) for the isotropic coding gain to exceed the separable coding gain.

A simple highly-effective method for progressive lossy-to-lossless coding of arbitrarily-sampled image data is proposed. This scheme is based on a recursive quadtree partitioning of the image domain along with an iterative sample-value averaging process. The proposed method is shown to offer much better progressive coding performance than a previously-proposed state-of-the-art coding method.

Sequential quadratic programming is used to design high-performance quincunx filter banks for image coding, where the resulting filter banks have perfect reconstruction, linear phase, high coding gain, good frequency selectivity, and certain prescribed vanishing-moment properties. Design examples are presented and compared to various previously proposed filter banks. The new filter banks are shown to be highly effective for image coding, outperforming previously proposed quincunx filter banks in most cases, and outperforming the well-known 9/7 filter bank in some limited cases.

A new technique is proposed for the design of high-performance quincunx filter banks for the application of image coding. This method yields linear-phase perfect-reconstruction systems with high coding gain, good analysis/synthesis filter frequency responses, and prescribed vanishing moment properties. Examples of filter banks designed with this technique are presented and shown to be highly effective for image coding.

In the case of one-dimensional filter banks, symmetric extension is a commonly used technique for constructing nonexpansive transforms of finite-length sequences. In this paper, we show how symmetric extension can be extended to the case of two-dimensional filter banks based on quincunx sampling. In particular, we show how, for filter banks of this type, one can construct nonexpansive transforms for input sequences defined on arbitrary rectangular regions.

JasPer, a portable, flexible, open-source, software tool kit for handling image data is described. This software provides a means for representing images, and facilitates the manipulation of image data as well as its import/export in various formats (such as JPEG 2000). JasPer is proving to be an extremely useful tool in a wide variety of applications, ranging from image coding/processing research to open-source and proprietary software development.

Studied are two lifting-based families of symmetry-preserving reversible integer-to-integer wavelet transforms. The transforms from both of these families are shown to be compatible with symmetric extension, which permits the treatment of arbitrary length signals in a nonexpansive manner. Throughout this work, particularly close attention is paid to rounding functions, and the properties that they must possess in various instances. Symmetric extension is also shown to be equivalent to constant per-lifting-step extension in certain circumstances.

The generalized S transform (GST), a family of reversible integer-to-integer transforms inspired by the S transform, is proposed. This family of transforms is then studied in some detail. For example, the relationship between the GST and lifting scheme is discussed, and the effects of choosing different GST parameters are examined. Some examples of specific transforms in the GST family are also given.

A software-based implementation of the image codec specified in the emerging JPEG-2000 standard is discussed. The run-time complexity and coding performance of this implementation are also analyzed.

In the context of image coding, a number of reversible integer-to-integer wavelet transforms are compared on the basis of their lossy compression performance, lossless compression performance, and computational complexity. Of the transforms considered, several were found to perform particularly well, with the best choice for a given application depending on the relative importance of the preceding criteria. Reversible integer-to-integer versions of numerous transforms are also compared to their conventional (i.e., nonreversible real-to-real) counterparts for lossy compression. At low bit rates, reversible integer-to-integer and conventional versions of transforms were found to often yield results of comparable quality. Factors affecting the compression performance of reversible integer-to-integer wavelet transforms are also presented, supported by both experimental data and theoretical arguments.

[Summary form only given]. There has been a growing interest in reversible integer-to-integer wavelet transforms for image coding applications. In this paper, a number of such transforms are compared on the basis of their objective and subjective lossy compression performance, lossless compression performance, and computational complexity. Of the transforms considered, several were found to perform particularly well, with the best choice for a given application depending on the relative importance of lossless compression performance, lossy compression performance, and computational complexity. Reversible integer-to-integer versions of numerous transforms are also compared to their conventional (i.e., nonreversible real-valued) counterparts for lossy compression. In many cases, the reversible integer-to-integer and conventional versions of a transform were found to yield results with comparable image quality.

In the context of image coding, a number of reversible integer-to-integer wavelet transforms are compared on the basis of their lossy compression performance, lossless compression performance, and computational complexity. Of the transforms considered, several were found to perform particularly well, with the best choice for a given application depending on the relative importance of the preceding criteria. Reversible integer-to-integer versions of numerous transforms are also compared to their conventional counterparts for lossy compression. At low bit rates, reversible integer-to-integer and conventional versions of transforms were found to often yield reconstructed images with comparable quality, both subjectively and objectively.

The performance of several decorrelating transforms is evaluated in the JPEG-2000 baseline system. The transforms considered are based on uniform parallel 2-channel and 8-channel filter banks and discrete cosine transform (DCT) building blocks. Through the analysis of lossy compression results, a system employing a combination of 8- channel and 2-channel filter banks is found to perform best overall. Also, the performance of several reversible transforms is evaluated in the same coding framework. Based on lossy and lossless compression results, a reversible version of the Cohen-Daubechies-Feauveau (2,2) wavelet transform was found to be most effective.