Departments of Statistics, Computer Science and the College

An approach to shape recognition using collections of randomized relational classification trees. The questions used to split the trees nodes on the training data involve global geometric arrangements of image tags, described in terms of relational graphs. The tags convey information about local subimage configurations.

At each tree node a huge family of admissible queries is defined, and only a small random sample is investigated to find the best one in terms of the drop in the conditional entropy of the distribution on classes. This randomization allows for the construction of a collection of weakly correlated trees. Classification of a test image is obtained by finding the mode of the sum of the terminal distributions on the classes reached by the image in each of these trees. These relational decision trees have been applied to handwritten character recognition, where classification rates of over 99% were achieved on the NIST database. For further details see

A thorough investigation into the properties of this algorithm in the presence of hundreds of shape classes and connections to brain function are described in

Currently we are exploring extensions to gray level images of 3d objects and to face identification in complex scenes.

These algorithms compute a smooth displacement field in two or three dimensions which is applied to a prototype image to yield a warped image as close as possible to some target image from the same image family. This has been applied to families of medical images: 2-d hand xrays, echocardiograms, 2-d MRI scans of the brain, and 3-d MRI scans. The computations involve the solution of a non-linear variational problem using spectral methods.

For further details see

For the applications of similar ideas in the context of emission tomography for the identification of tumors, see

A prior distribution or cost function is defined on deformations of a graphical template of landmarks constructed from triangles, which penalizes deviations of shape of these triangles. A simple likelihood of the data given the landmark locations is formulated, using robust local operators. An image is scanned for candidates of each of the landmarks. The algorithm picks out the collection of candidates for which the penalty of the match is minimal using dynamic programming on decomposable graphs. This approach yields precise matches of landmarks of interest, and provides an object specific parameterization of shape variation. It provides a generic toolbox for modeling shape in a variety of applications. These models have been applied to hand xrays and different views of MRI brain scans and provide a means for automatic anatomy identification. See image above.

For further details see

Recently in Recurrent network of perceptrons with three state synapses we discovered that a slight modification of the above networks yields much more powerful classifiers. Instead of two-state synapses (0/1) connecting the input feature layer to the output layer we use three-state (0/1/2) synapses together with feed-forward inhibition that makes the effective weights of the synapses (-1/0/1). This small modification allows the learning algorithm to separate two types of informative features - those that are high probability on class and low probability off class (for which the synaptic state becomes 1), and those with low probability on class and high probabilty off class (for which the synaptic state becomes -1). All non-informative features end up with synaptic state 0. In addition adding inhibition in the attractor layer allows for stable recurrent dynamics in which the class with most active neurons remains active and all others class neurons are inactivated.

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