Michael D. Adams

Reversible integer-to-integer wavelet transforms for image compression: performance evaluation and analysis

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.

JasPer: a software-based JPEG-2000 codec implementation

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.

JasPer: a portable flexible open-source software tool kit for image coding/processing

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.

Symmetric-extension-compatible reversible integer-to-integer wavelet transforms

Symmetric extension is explored as a means for constructing nonexpansive reversible integer-to-integer (ITI) wavelet transforms for finite-length signals. Two families of reversible ITI wavelet transforms are introduced, and their constituent transforms are shown to be compatible with symmetric extension. One of these families is then studied in detail, and several interesting results concerning its member transforms are presented. In addition, some new reversible ITI structures are derived that are useful in conjunction with techniques like symmetric extension. Last, the relationship between symmetric extension and per-lifting-step extension is explored, and some new results are obtained in this regard.

Wavelet transforms in the JPEG-2000 standard

Numerous issues associated with wavelet transforms in the JPEG-2000 Part-1 standard (i.e., ISO/IEC 15444-1) are studied. The dynamic range of wavelet transform coefficients and computational complexity of wavelet transforms are examined. Also, the effect of wavelet transforms on coding efficiency is investigated. The information presented may prove beneficial to those developing JPEG-2000 codec implementations.

Generalized S transform

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 detail by considering topics such as GST parameter calculation, the effects of using different rounding operators in the GST, and the relationship between the GST and the lifting scheme. Some examples of specific transforms in the GST family are also given. In particular, a new transform in this family is introduced, and its practical utility is demonstrated.

A Flexible Content-Adaptive Mesh-Generation Strategy for Image Representation

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 , 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.

Optimal design of high-performance separable wavelet filter banks for image coding

An optimization-based method is proposed for the design of high-performance separable wavelet filter banks for image coding. This method yields linear-phase perfect-reconstruction systems with high coding gain, good frequency selectivity, and certain prescribed vanishing-moment properties. Several filter banks designed with the proposed method are presented and shown to work extremely well for image coding, outperforming the well-known 9/7 filter bank from JPEG 2000 in most cases. With the proposed design method, the coding gain can be maximized with respect to the separable or isotropic image model, or jointly with respect to both models. The joint case, which is shown to be equivalent to the isotropic case, is experimentally demonstrated to lead to filter banks with better average coding performance than the separable case. During the development of the proposed design method, filter banks from a certain popular separable two-dimensional (2D) wavelet class (to which our optimal designs belong) were observed to always have a higher coding gain with respect to the separable image model than with respect to the isotropic one. This behavior is examined in detail, leading to the conclusion that, for filter banks belonging to the above class, it is highly improbable (if not impossible) for the isotropic coding gain to exceed the separable coding gain.

A Tuned Mesh-Generation Strategy for Image Representation Based on Data-Dependent Triangulation

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.

An Efficient Progressive Coding Method for Arbitrarily-Sampled Image Data

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.