General Coordinate Invariant Image Smoothing Using a Metric Tensor
Takashi Toriu · 2020
Images are often deformed for various reasons such as viewpoint movement, lens distortion, etc. It is desirable that image processing is invariant for such deformation. This paper proposes a new image smoothing which is invariant under general coordinate transformations. General coordinate transformation is a continuous coordinate transformation defined by differentiable function. To realize general coordinate transformation invariance, we introduce the metric tensor which transforms appropriately for the general coordinate transformation. Using the metric tensor, we define a general coordinate invariant evaluation function. General coordinate invariant smoothing is achieved by a process of minimizing the evaluation function. Effectiveness of the proposed method is confirmed by computer experiments.