The Signed Cumulative Distribution Transform for 1-D signal analysis and classification

This paper presents a new mathematical signal transform that is especially suitable for decoding information related to non-rigid displacements. We provide measure theoretic framework extend the existing Cumulative Distribution Transform [ACHA 45 (2018), no. 3, 616-641] arbitrary (signed) signals on $\overline{\mathbb{R}}$. present both forward (analysis) and inverse (synthesis) formulas transform, describe several of its properties including translation, scaling, convexity, linear separability others. Finally, we metric in space, demonstrate application classifying (detecting) under random