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Global optimization using data driven local metrics


Background

Starting with investigating a formulation in regularization of displacement fields in image registration and successful implementation of said method, the GLO (Global Linear Optimization) project was started.



Short introduction

The GLO method solves a linear least squares problem with respect to an application-specific metric. In general we want our metric to result in a sparse matrix representation if possible. One obvious way to do this is to connect spatially neighboring data points with a local metric. The equation system includes all data points in some sense and optimizes a new data set from the metric and some old data. Since our objective vector is so big, it is from a computational standpoint more and more important that our metric is sparse - that is - few dependences between data points (compared to the total data set size). So far, local structure tensor information has been used together with this method in adaptive filtering of displacement fields in image registration as well as image enhancement.

Application - Regularization in Image Registration

This application was presented in poster format at the IEEE conference ICIP 2012 in Florida, USA. Still waiting for the paper to show up in IEEEexplore... One big pro of this approach compared to many purely local method: Does not need any advanced iteration schemes and propagation of certain data, because this information is automatically incorporated in the equation system and then "propagated" when solving it.

        
                                           Before Regularization                                     After Global Regularization

Application - Image Enhancement

The Image Enhancement method "Global Linear Optimization - Local Structure Tensor Metric" (GLO-LoSTM) is implemented, submitted and awaiting review. Some preliminary results are found below. Even though we use a very local metric, we get are able to get preliminary results which are comparable to some very high performing non-local methods of the later years.

           
      Noisy image, std dev = 20                           Image Enhanced with GLO-LoSTM
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