Segmentation is often an essential intermediate step in image analysis. A volume segmentation characterizes the underlying volume image in terms of geometric information--segments, faces between segments, curves in which several faces meet--as well as a topology on these objects. Existing algorithms encode this information in designated data structures, but require that these data structures fit entirely in Random Access Memory (RAM). Today, 3D images with several billion voxels are acquired, e.g. in structural neurobiology. Since these large volumes can no longer be processed with existing methods, we present a new algorithm which performs geometry and topology extraction with a runtime linear in the number of voxels and log-linear in the number of faces and curves. The parallelizable algorithm proceeds in a block-wise fashion and constructs a consistent representation of the entire volume image on the hard drive, making the structure of very large volume segmentations accessible to image analysis. The parallelized C++ source code, free command line tools and MATLAB mex files are avilable from this http URL
The main focus of previous efforts to extract and encode the geometry and topology of segmentations has not been on large volume segmentations but on the efficient processing of the merging and splitting of segments. These operations are required within the context of inter-active segmentation. In @cite_0 @cite_1 , representations of the geometry and topology are constructed incrementally, using random access to already constructed parts of the data structure. In order for these algorithms to work efficiently, the underlying data structures need to be kept entirely in RAM. To extract the geometry and topology of a volume segmentation of @math voxels, @math bytes @math GB of RAM are required for the labeling of the topological grid, an amount that is not available on present day desktop computers. Beyond @math voxels, even the @math TB of RAM of a large server are insufficient. The method presented in this article overcomes this limitation by means of block-wise processing. It makes geometry and topology extraction from large volume segmentations possible.
@cite_0 @cite_1
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Although many interactive segmentation methods exists,none can be considered a silver bullet for all clinical tasks. Moreover, incompatible data representations prevent multiple algorithms from being combined as desired. We propose the GEOMAP as a unified representation for segmentation results and illustrate how it facilitates the design of an integrated framework for interactive medical image analysis. Results show the high flexibility and performance of the new framework. In this paper, we define the three-dimensional topological map, a model which represents both the topological and geometrical information of a three-dimensional labeled image. Since this model describes the image's topology in a minimal way, we can use it to define efficient image processing algorithms. The topological map is the last level of map hierarchy. Each level represents the region boundaries of the image and is defined from the previous level in the hierarchy, thus giving a simple constructive definition. This model is an extension of the similar model defined for 2D images. Progressive definition based on successive map levels allows us to extend this model to higher dimension. Moreover, with progressive definition, we can study each level separately. This simplifies the study of disconnection cases and the proofs of topological map properties. Finally, we provide an incremental extraction algorithm which extracts any map of the hierarchy in a single image scan. Moreover, we show that this algorithm is very efficient by giving the results of our experiments made on artificial images.