Improve performance and reduce memory overhead of symmetric eigenvalue computations

[grlee77]

Description:

hessian_matrix_eigenvalues has an efficient, analytical code path for 2D, but for nD the current implementation is very memory-hungry. Internally arrays of shape: image.shape + (image.ndim, image.ndim) get passed to cp.linalg.eigvalsh, so memory requirements grow rapidly with ndim.

The same underlying innefficiency applies to several other functions relying on the same symmetric eigenvalue computations:

• skimage.feature.blob_doh
• skimage.feature.multiscale_basic_features
• skimage.feature.shape_index
• skimage.feature.structure_tensor_eigenvalues
• skimage.filters.frangi
• skimage.filters.hessian
• skimage.filters.meijering
• skimage.filters.sato

For the 3D case, I recently implemented a memory-efficient analytical solution downstream in cuCIM. It is also much faster using an analytical solution than relying on a general eigenvalue solver.

For the nD case, I don't know of any analytical solution. I think the easiest workaround in that case is to divide up the eigenvalue computations to only operate on subsets of the image at a time to reduce the overhead. e.g. using dask.array.map_blocks. Each pixel is computed independently of the others so the blocks do not need to be overlapping.

[github-actions]

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