Image inpainting is the process to modify an image in an undetectable form. From this point of view image inpainting is a process to build an image, with the pixels (patch) in source region. The tecnhique most extended consists in to copy patches from the source region to the target region with the objective generating a 'realistic' image. The first problem, with this technique, is to determine the patching priority. In [1] and [2] establish the priority as a trade off between two terms: data term and confidence term. The data term describes how strong the isophote hitting the boundary and the confidence term indicates how many existing pixels are there in a patch. Next, these methods patches the target region by the most similar area in the know image. In [2] the similarity of two regions is computed by the sum of squared differences (SSD) of already filled pixels in them. This searching can not perseve the linear structure of the image, obtaining an image with artifacts. In Figure 1 is show in (A) the Kanizsa Triangle, in which we have to patch the zone green in (B).In this image, only two levels of grey are used, black and white. For it, according to 'The Connectivity Principle' of the human disocclusion process, human mostly seem to prefer the connected result. However, in Figure 1.(A) you have two patches with the same SSD value if you don't have a mechanism which process this ambiguous situation, the election carry out to an image with artifacts. Following to 'The Connective Principle' the system must chose the Ψ_q2, given the (D) output image.

Fig1: (A) Original image: Ψ_p target patch and Ψ_q1 and Ψ_q2 two source targets.
(B) Target region in green.
(C) Output if the source target selected is Ψ_q1.
(D) Output if the source target selected is Ψ_q2

Therefore, a manner image inpainting without artifacts is preserving the linear structure and texture of the original image. A linear structure is associated with transients in the image. Here, transients is refered to coefficients with high values around coefficients with medium and low values. Thus, to distinguish if a patch form part of a linear structure is equivalent to know where are the transients associated to the linear structure. This problem can be resolved with different transforms: Gabor, Wavelet or Contourlet transform. In this work we have used the Nonsubsampled Contourlet Transform (NSCT) [3] to distinguish where are the transients in an image. The main characterists are:

• Efficient:This transform represents edges and other singularites along curves much more efficently (i.e. using fewer coefficients) than other transforms.
• Shift invariance: A small shift of the input signal produce a small shift in the output signal.
• Multiscale decomposition: This transform give information of the input signal at different orientations and scales.
• Redundance:It is a overcomplete transform

In this work we have focused over two aspects:

• Selecting the higher priority patch with center at p. Thus, we have given a new definition of the data term based on the redundancy, across orientations and scales in the NSCT domain, of the corner pixels located at the boundary of the target region. It follows that a pixel with a high value for the data term means that: (i) There is a corner point at a particular scale, since the high energy level is achieved when two bands of equal scale at different orientations meet at this particular spatial location; and (ii) this same corner point must be present across different scales. The interesting point is that pixels in the boundary of the target region which are part of broken or occluded features (e.g., broken edges) have a high value of the data term, and thus, they are identified as corner points.
• Obtaining the source patch to be copied onto the target patch. Concerning the source-patch selection, we have shown that by only using the Square Sum Differences between target and source patch, it can produce results with artefacts (see Fig1). To overcome this problem, a new mechanism of source patch selection has been proposed in this work. Firstly we obtain the set of the most similar source patches to the target patch by using the Square Sum Differences. Next, from this set, we select the patch achieving the minimum dispersion across orientations and scales when is copied onto the target patch, which maintains the transients of the original image while avoiding new ones. Hence, the selected source patch continues the broken features in the original image while avoiding the formation of artefacts.

Bibliography

Acknowledgments. This work was sponsored by the Spanish Board for Science and Technology (MICINN) under grant TIN2010-15157 cofinanced with FEDER funds.