@mastersthesis {xGiro-i-Nieto00, title = {Volumetric Data Compression based on Cube-Splitting and Embedded Block Coding by Optimized Truncation}, year = {2000}, abstract = {

Many medical data acquisition devices or multispectral imaging techniques produce three-dimensional image data. These images must be stored in limited space devices or transmitted through limited bandwidth channels. Compression techniques are an extremely valuable tool to reduce the expensive resource requirements.

However, compression techniques have already been developed for the more popular two-dimensional images. Splitting the volumetric image in slices and applying a two- dimensional coding technique to each slice is the philosophy followed by the classical approach for 3D compression. This is clearly inefficient, because 2D techniques only exploit the image correlation in the X and Y axis. In volumetric images a new Z-axis appears, whose correlation must be also exploited to achieve the best results.

The basis for all current image and video compression standards is DCT-based coding. For these techniques the computation is based on splitting of the image into NxN blocks and transforming it from the spatial domain into the DCT domain. Typical examples are first generation coders, like JPEG, which produce a non-structured, unique bit-stream. This technique could easily be adapted to three-dimensional by splitting the volume into NxNxN blocks and applying a 3D DCT. However, one encounters two problems. First, the DCT transform is a lossy, and medical practice cannot tolerate any distortion that could lead to an faulty diagnose. Secondly, contemporary transmission techniques make use of concepts like rate-scalability, quality and resolution scalability, features that are not fully supportable by DCT techniques.

Coders using a wavelet transform as front-end are good candidates to overcome these problems. They scan each bit-planes one by one to generate a structured bit-stream. This bit-stream can be truncated to give more or less quality or resolution, and they are classified second-generation coders. A typical example of 3D wavelet coding is the octave zero-tree based coding [Bil99, Xio99, Kim99, Kim00, Sch00a], which currently tends to deliver the best compression performance. However, it is difficult to control the bit-stream structure since it is dependent on the coder{\textquoteright}s data flow.

The new image compression standard JPEG2000 uses a third generation technique, called EBCOT ,incorporating an abstract interface to enable reordering of the generated code packages. In this way a fully controllable bit-stream structure is achieved. For example, the bit-stream can be equipped so that resolution or quality scalability are supported. The current verification model (VM7.0) of JPEG2000 however, does not include three-dimensional coding. The only support that is given for multidimensional and/or multi-spectral images is the possibility to execute a wavelet transform along the component axis. Unfortunately, the code supporting this feature was still buggy at the time this document was written

Adapting this third-generation coding technique to a three-dimensional environment was the aim of this thesis. The input volume is transformed into the wavelet transform with the 3D Wavelet front-end described and implemented by Schelkens et al. [Sch00a] and Barbarien [Joeri{\textquoteright}s thesis]. Later it is coded by an hybrid technique of Cube-Splitting and an JPEG2000{\textquoteright}s EBCOT module, modified to support the third dimension. The Cube-Splitting module codes big zero-volumes very efficiently, while the EBCOT coder is responsible for the coding of the (sub)volumes containing significant samples. Hence, the implemented coder is called CS- EBCOT.\ 

}, keywords = {coding, volumetric coding}, author = {Xavier Gir{\'o}-i-Nieto} }