1. A method for compressing a deep image comprising a plurality of voxels, comprising: for each of the plurality of voxels, converting, by a processor, a matrix representation of a voxel value to a corresponding value in a Lie algebra based on a logarithmic mapping function applied to a matrix exponential of the matrix representation of the voxel value, wherein each matrix representation of the voxel value is stored in a computer readable medium and represents digital computer graphics data; 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 respective difference between the interpolation of each value in the first subset and the corresponding value in the first subset 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.