A Fast and Memory Efficient Stationary Wavelet Transform for 3D Cell Segmentation

Wavelet approaches have proven effective in many segmentation applications and in particular in the segmentation of cells, which are blob-like in shape. We build upon an established wavelet segmentation algorithm and demonstrate how to overcome some of its limitations based on the theoretical derivation of the compounding process of iterative convolutions. We demonstrate that the wavelet decomposition can be computed for any desired level directly without iterative decompositions that require additional computation and memory. This is especially important when dealing with large 3D volumes that consume significant amounts of memory and require intense computation. Our approach is generalized to automatically handle both 2D and 3D and also implicitly handles the anisotropic pixel size inherent in such datasets. Our results demonstrate a 28X improvement in speed and 8X improvement in memory efficiency for standard size 3D confocal image volumes without adversely affecting the accuracy.