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Reconstruction of images from Gabor Wavelet coefficients
Michael Pötzsch
Thomas Maurer
Christoph von der Malsburg

For visualization purposes and for applying transformations to an image after it has been transformed by a set of linear filters, it is important to be able to reconstruct the image from transformed data faithfully. Reconstruction is trivial if the filters are orthogonal. For affine sets of filters, such as the Gabor wavelets, an orthogonalization procedure needs to be employed a posteriori. We have developed a method that can also be applied to a sparse subset of transformed data as required for labeled graphs.

reconstruction of images from transformed data (23 kB)

Figure 1: Different reconstruction methods for one location. First column: Original images with the central pixel marked by a cross. Second column: Reconstructions from the full Gabor wavelet transform, i.e. at all pixel positions. Third column: Reconstructions from one jet, i.e. the Gabor wavelet transform at the central pixel only. Last column: Reconstructions from one jet if the affine properties of the Gabor transform are not taken into account, i.e. if it is done the naive way.

face graph (10 kB)reconstruction from face graph (13 kB)reconstruction from face bunch 
graph (13 kB)

Figure 2: Reconstruction methods for a graph. Left: A face with a graph, which is labeled with Gabor jets. Middle: A reconstruction of the image from the graph. Right: A reconstruction of the image from a face bunch graph, i.e. no information from the original image has been used but only the best fitting jets of a set of 100 other faces.

The Institut für Neuroinformatik (INI) is a central research unit of the Ruhr-Universität Bochum. We aim to understand the fundamental principles through which organisms generate behavior and cognition while linked to their environments through sensory systems and while acting in those environments through effector systems. Inspired by our insights into such natural cognitive systems, we seek new solutions to problems of information processing in artificial cognitive systems. We draw from a variety of disciplines that include experimental approaches from psychology and neurophysiology as well as theoretical approaches from physics, mathematics, electrical engineering and applied computer science, in particular machine learning, artificial intelligence, and computer vision.

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