  Numerical difference computation is one of the cores and indispensable in the
modern digital era. Tao general difference (TGD) is a novel theory and approach
to difference computation for discrete sequences and arrays in multidimensional
space. Built on the solid theoretical foundation of the general difference in a
finite interval, the TGD operators demonstrate exceptional signal processing
capabilities in real-world applications. A novel smoothness property of a
sequence is defined on the first- and second TGD. This property is used to
denoise one-dimensional signals, where the noise is the non-smooth points in
the sequence. Meanwhile, the center of the gradient in a finite interval can be
accurately location via TGD calculation. This solves a traditional challenge in
computer vision, which is the precise localization of image edges with noise
robustness. Furthermore, the power of TGD operators extends to spatio-temporal
edge detection in three-dimensional arrays, enabling the identification of
kinetic edges in video data. These diverse applications highlight the
properties of TGD in discrete domain and the significant promise of TGD for the
computation across signal processing, image analysis, and video analytic.
