Images, 2D or 3D, are usually perceived or analyzed in their
respective number of dimensions either in the spatial domain or
frequency domain. 3D images such as volumetric data sets are
important in many scientific and biomedical fields. To extend a 2D
image compression coder to 3D, special care is often required. We
are proposing a progressive lossy to lossless image coder that can
be extended to multi-dimensions with minimum effort. Hilbert
traversal enables us to transform a multi-dimensional signal to a
1D signal, thus 2D/3D images can be compressed in the same way.
Only the traversal program needs to be modified for images in
different dimensions. Hilbert traversal's locality and slow
context change properties render a very compressible 1D signal.
After integer wavelet transformation, the resulting wavelet
coefficients are rearranged based on our new linearization
algorithm. The most important information appears in the front of
the data stream. Progressive image encoding/decoding, which is
desired by many applications, is possible due to the linearization
algorithm. The control data and wavelet coefficients are finally
entropy coded to produce a compact data stream. Lossy and lossless
image information is embedded in the same data stream.
The volumetric data set is important in many scientific and biomedical fields. Since such sets may be extremely large, a compression method is critical to store and transmit them. To achieve a high compression rate, most of the existing volume compression methods are lossy, which is usually unacceptable in biomedical applications. We developed a new context-based non-linear prediction method to preprocess the volume data set in order to effectively lower the prediction entropy. The prediction error is further encoded using Huffman code. Unlike the conventional methods, the volume is divided into cubical blocks to take advantage of the data’s spatial locality. Instead of building one Huffman tree for each block, we developed a novel binning algorithm that build a Huffman tree for each group (bin) of blocks. Combining all the effects above, we achieved an excellent compression rate compared to other lossless volume compression methods. In addition, an auxiliary data structure, Scalable Hyperspace File (SHSF) is used to index the huge volume so that we can obtain many other benefits including parallel construction, on-the-fly accessing of compressed data without global decompression, fast previewing, efficient background compressing, and scalability etc.
In this paper, we present a neuro-medical imaging system called the Brain Slicer, which allows neuroscientists to construct a three-dimensional digital brain atlas from an array of high-resolution parallel section images and obtain arbitrary oblique section images from the digital atlas. This application is based on a new data structure, the Scalable Hyper-Space File (SHSF). The SHSF is a generalized data structure that can represent a hyperspace of any dimension. The two-dimensional SHSF is a scalable linear quadtree and the three-dimensional SHSF is a scalable linear octree. Unlike the normal linear quadtree and octree, the data structure uses a scalable linear coding scheme. It recursively uses fixed-length linear code to encode the hyperspace, which is efficient in terms of storage space and accessing speed. The structure lends itself well to pipelined parallel operations in constructing the volumetric data set, so that it enjoys excellent performance even though the huge data set imposes heavy disk I/O requirements. The data structure can provide different levels of detail; therefore it can be used in an environment where the bandwidth and computation power is limited, such as the Internet and slow desktop computers. We envision that this methodology can be used in many areas other than neuro-medical imaging.
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