Image warp preserving content intensity
This addresses the need for intensity-preserving image warping in quantitative analysis fields such as optics and material science, representing an incremental improvement over existing techniques.
The paper tackles the problem of image warping by introducing a method that preserves the total intensity of the transformed image, ensuring quantitative accuracy for applications like measuring radiances or optical fluxes. The result is quantitatively exact under assumptions of constant image density within pixels and diffeomorphic transformations.
An accurate method for warping images is presented. Differently from most commonly used techniques, this method guarantees the conservation of the intensity of the transformed image, evaluated as the sum of its pixel values over the whole image or over corresponding transformed subregions of it. Such property is mandatory for quantitative analysis, as, for instance, when deformed images are used to assess radiances, to measure optical fluxes from light sources, or to characterize material optical densities. The proposed method enforces area resampling by decomposing each rectangular pixel in two triangles, and projecting the pixel intensity onto half pixels of the transformed image, with weights proportional to the area of overlap of the triangular half-pixels. The result is quantitatively exact, as long as the original pixel value is assumed to represent a constant image density within the pixel area, and as long as the coordinate transformation is diffeomorphic. Implementation details and possible variations of the method are discussed.