We wish to match sets of images to sets of images where both sets are undergoing various distortions such as viewpoint and lighting changes.

Recently, research in the field of content-based image retrieval has attracted a lot of attention. Nevertheless, most existing methods cannot be easily applied to medical image databases, as global image descriptions based on color, texture, or shape do not supply sufficient semantics for medical applications. The concept for content-based image retrieval in medical applications (IRMA) is therefore based on the separation of the following processing steps: categorization of the entire image; registration with respect to prototypes; extraction and query-dependent selection of local features; hierarchical blob representation including object identification; and finally, image retrieval. Within the first step of processing, images are classified according to image modality, body orientation, anatomic region, and biological system. The statistical classifier for the anatomic region is based on Gaussian kernel densities within a probabilistic framework for multiobject recognition. Special emphasis is placed on invariance, employing a probabilistic model of variability based on tangent distance and an image distortion model. The performance of the classifier is evaluated using a set of 1617 radiographs from daily routine, where the error rate of 8.0% in this six-class problem is an excellent result, taking into account the difficulty of the task. The computed posterior probabilities are furthermore used in the subsequent steps of the retrieval process.

When dealing with pattern recognition problems one encounters different types of a-priori knowledge. It is important to incorporate such knowledge into the classification method at hand. A very common type of a-priori knowledge is transformation invariance of the input data, e.g. geometric transformations of image-data like shifts, scaling etc. Distance based classification methods can make use of this by a modified distance measure called tangent distance [13, 14]. We introduce a new class of kernels for support vector machines which incorporate tangent distance and therefore are applicable in cases where such transformation invariances are known. We report experimental results which show that the performance of our method is comparable to other state-of-the-art methods, while problems of existing ones are avoided.

One fundamental problem in image recognition is to establish the resemblance of two images. This can be done by searching the best pixel to pixel mapping taking into account monotonicity and continuity constraints. We show that this problem is NPcomplete by reduction from 3-SAT, thus giving evidence that the known exponential time algorithms are justi ed, but approximation algorithms or simpli cations are necessary.

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We evaluate different two-dimensional non-linear deformation models for handwritten character recognition. Starting from a true two-dimensional model, we derive pseudo-two-dimensional and zero-order deformation models. Experiments show that it is most important to include suitable representations of the local image context of each pixel to increase performance. With these methods, we achieve very competitive results across five different tasks, in particular 0.5 % error rate on the MNIST task. 1

The principle of maximum entropy is a powerful framework that can be used to estimate class posterior probabilities for pattern recognition tasks. In this paper, we show how this principle is related to the discriminative training of Gaussian mixture densities using the maximum mutual information criterion. This leads to a relaxation of the constraints on the covariance matrices to be positive (semi-)definite.

. In this paper, we present a mixture density based approach to invariant image object recognition. To allow for a reliable estimation of the mixture parameters, the dimensionality of the feature space is optionally reduced by applying a robust variant of linear discriminant analysis. Invariance to ane transformations is achieved by incorporating invariant distance measures such as tangent distance. We propose an approach to estimating covariance matrices with respect to image variabilities as well as a new approach to combined classication, called the virtual test sample method. Application of the proposed classier to the well known US Postal Service handwritten digits recognition task (USPS) yields an excellent error rate of 2:2%. We also propose a simple, but eective approach to compensate for local image transformations, which signicantly increases the performance of tangent distance on a database of 1,617 medical radiographs taken from clinical daily routine. Keywords: statistical pattern recognition, density estimation, invariant image object recognition, combined classication

Statistical classification using tangent vectors and classification based on local features are two successful methods for various image recognition problems. These two approaches tolerate global and local transformations of the images, respectively. Tangent vectors can be used to obtain global invariance with respect to small affine transformations and line thickness, for example. On the other hand, a classifier based on local representations admits the distortion of parts of the image.