The modelling of three-dimensional (3D) objects with triangular meshes represents a major interest for medical imagery. Indeed, visualization and handling of 3D representations of biological objects (like organs for instance) are very helpful for clinical diagnosis, telemedicine applications, or clinical research in general. Today, the increasing resolution of imaging equipments leads to densely sampled triangular meshes, but the resulting data are consequently huge. In this chapter, we present one specific lossy compression algorithm for such meshes that could be used in medical imagery. According to several state-of-the-art techniques, this scheme is based on wavelet filtering, and an original bit allocation process that optimizes the quantization of the data. This allocation process is the core of the algorithm, because it allows the users to always get the optimal trade-off between the quality of the compressed mesh and the compression ratio, whatever the user-given bitrate. By the end of the chapter, experimental results are discussed and compared with other approaches.
Top1.2 Introduction
The surface of a 3D object is most of times represented by a triangular mesh (see Figure 1). A triangular mesh is a set of triangles (defined by the 3D positions of three vertices in the space), and connected by their common edges. Generally, the triangular meshes are irregular, meaning that all the vertices do not have the same number of neighbours (each vertex of a regular mesh has 6 neighbours).
Figure 1. 3D modelling of a tooth (on the left) defined by a triangular mesh (on the right)
In medical imagery and numerous other domains, the resolution of 3D representations has to be high, in order to get the maximum of geometrical details. But designing such detailed surfaces leads to triangular meshes which can be defined today by several millions of vertices. Unfortunately, a raw representation of these densely sampled meshes is huge, and it can be a major drawback for an efficient use of such data. For instance:
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archival or storage of a large quantity of similar data in a patient database is problematic (capacity of the servers);
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during clinical diagnosis or follow-up cares of patients, a remote access to database in particular with bandwidth-limited transmission systems, will be long and unpleasant for practitioners;
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real-time and bandwidth-limited constraints in general could restrict the applications in the domain of telemedicine.
In signal processing, compression is a relevant solution to allow a compact storage, an easy handling or a fast transmission in bandwidth-limited applications of large data. Two kinds of compression methods exist: the lossless and the lossy methods. With a lossless method, all original data can be recovered when the file is uncompressed. On the other hand, lossy compression reduces data by permanently eliminating certain information, especially irrelevant information. In this case, when the file is decompressed, the data may be different from the original, but close enough to be still useful. Lossy methods can produce a much smaller compressed file than any known lossless method, while still meeting the requirements of the application. Consequently, they always attempt to optimize the trade-off between bitrate (relative to the file size) and quality of compressed data (relative to the information loss).
When dealing with large data like densely sampled triangular meshes for instance, lossy methods are more relevant since it allows reaching higher compression ratios. However, in the domain of medical imagery, eliminating crucial geometrical details may be damaging, since it may lead, for instance, to false clinical diagnosis. Therefore the information loss must be absolutely well-controlled and also limited when compressing medical data.
One relevant way to overcome this crucial problem is to include an allocation process in the compression algorithm. The purpose of this process is generally to optimize lossy compression by minimizing the losses due to data quantization for one specific bitrate. But designing a fast and low-complex allocation process is not trivial. Therefore, in this chapter, we particularly explain how designing an allocation process for an efficient coding of large surface meshes.
The remainder of this chapter is organized as follows. Section 3 gives a short survey of the main methods of compression for 3D surface meshes. Section 4 introduces an overview of the proposed coder/decoder, the problem statement relative to the allocation process, and the major contributions of this work. In section 5 we detail the proposed bit allocation, and present a model-based algorithm in section 6. Then, we give some experimental results and discuss the advantages/disadvantages of this method in section 7. Finally, we conclude in section 8, and highlight the main future research directions in section 9.