M.Sc Thesis

M.Sc StudentHyams Yedidya
SubjectOn the Spatial Distribution of Colour in Images and its Role
in Image Resizing
DepartmentDepartment of Electrical and Computer Engineering
Supervisor ASSOCIATE PROF. Moshe Porat


This thesis addresses the process of sampling and demosaicing occurring in the vast majority of digital colour cameras. Much has been written about the process of sampling in the Fourier domain. The main weakness of the Fourier domain is its global strictest conditions. In addition, while it provides high certainty in the spectral domain it gives none in the spatial domain.

In this work we lay out a new framework answering both flaws using a total variation

(TV) approach. The high certainty in the spatial domain of this transform allows local properties to be exploited into local reconstruction conditions. The calculation of the missing interpolated pixels is carried out by determining which of the neighbouring pixels has a similar behaviour in the spectral TV scale space at scales not affected by the sampling process. Choosing the correct neighbour enables us to reconstruct the un-sampled pixels based on the pixel with the highest matching spectral properties.  This understanding of the sampling process helps define a local adaptive filter for reconstructing the image. This adaptivity of the filter is to the extent of choosing the scales relevant to the image per-pixel while omitting scales matching with the sampling mesh. Such intimate reconstruction allows for fine filtering where needed along with a coarser filtering in other image sections all dependent on the information in that area. This research not only serves as a demosaicing application but also sheds light on the behaviour of the spectral TV transform under sampling.