  Topological integral transforms have found many applications in shape
analysis, from prediction of clinical outcomes in brain cancer to analysis of
barley seeds. Using Euler characteristic as a measure, these objects record
rich geometric information on weighted polytopal complexes. While some
implementations exist, they only enable discretized representations of the
transforms, and they do not handle weighted complexes (such as for instance
images). Moreover, recent hybrid transforms lack an implementation.
  In this paper, we introduce Eucalc, a novel implementation of three
topological integral transforms -- the Euler characteristic transform, the
Radon transform, and hybrid transforms -- for weighted cubical complexes.
Leveraging piecewise linear Morse theory and Euler calculus, the algorithms
significantly reduce computational complexity by focusing on critical points.
Our software provides exact representations of transforms, handles both binary
and grayscale images, and supports multi-core processing. It is publicly
available as a C++ library with a Python wrapper. We present mathematical
foundations, implementation details, and experimental evaluations,
demonstrating Eucalc's efficiency.
