  Digital image inpainting refers to techniques used to reconstruct a damaged
or incomplete image by exploiting available image information. The main goal of
this work is to perform the image inpainting process from a set of sparsely
distributed image samples with the Smoothed Particle Hydrodynamics (SPH)
technique. As, in its naive formulation, the SPH technique is not even capable
of reproducing constant functions, we modify the approach to obtain an
approximation which can reproduce constant and linear functions. Furthermore,
we examine the use of Voronoi tessellation for defining the necessary
parameters in the SPH method as well as selecting optimally located image
samples. In addition to this spatial optimization, optimization of data values
is also implemented in order to further improve the results. Apart from a
traditional Gaussian smoothing kernel, we assess the performance of other
kernels on both random and spatially optimized masks. Since the use of
isotropic smoothing kernels is not optimal in the presence of objects with a
clear preferred orientation in the image, we also examine anisotropic smoothing
kernels. Our final algorithm can compete with well-performing sparse inpainting
techniques based on homogeneous or anisotropic diffusion processes as well as
with exemplar-based approaches.
