Systems, method, and computer program products for compressing a deep image comprising a plurality of voxels by, for each of the plurality of voxels, converting a voxel value to a corresponding value in a Lie algebra based on a logarithmic mapping function, interpolating a first subset of the plurality of values in the Lie algebra using a linear interpolation function applied to a first endpoint and a second endpoint of a first voxel column of the deep image, and upon determining that a deviation of the interpolation of each value in the first subset of the plurality of values does not exceed a threshold, storing an indication of the first endpoint, the second endpoint, and the respective values in the Lie algebra corresponding to the first and second endpoints.