Computer Vision News - December 2016

Computer Vision News Computer Vision News Research 31 Research Challenge: Continuous-domain visual signals are usually captured as discrete (digital) images. In general, this operation is not invertible, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image, unless it satisfies certain constraints (e.g. band limitedness). The challenge is how to recover the shapes directly from the pixel data , without intermediate curve fitting steps or the band limitedness assumption, usually used for this purpose. Novelty: The problem of reconstructing a continuous-domain shape from a gray-scale discrete image is essentially equivalent to the interpolation of pixels in a way that generates a binary image. The authors of Shapes From Pixels formulate this as a minimization problem , where the domain is the sampling kernels and the constraints encode the sampling relation. The minimizers will be shapes with minimum perimeter and smooth boundaries. However, this is a non-convex, computationally intractable, problem. The authors introduce a reducibility condition on the sampling of the discrete image and prove that, when it is satisfied, the problem becomes convex. Method: I(x,y) denotes the continuous image with pixel values in the range Ω=[1,0]2. D denotes the discrete image (m×m-pixel). In the consistent image recovery problem, we seek the approximation of the original image that generates the same measurement pixels. We can relate the d ij , 1 ≤ i, j ≤ m of D to the image I(x, y) as: where T is the sampling period. The equivalent representation of index of d ij in the vertical raster scan of D is defined as follows: Where k=(j-1)m+i, 1≤k≤m 2 and f k is the sampling kernel associated with d k . Next, the authors define the set of all non-negative-valued images over Ω that are consistent with 1≤ ≤ 2 as: