In this paper, we introduce a new classification algorithm called the optimization of distribution differences (ODD). The algorithm aims to find a transformation from the feature space to a new space where the instances in the same class are as close as possible to one another, whereas the gravity centers of these classes are as far as possible from one another. This aim is formulated as a multiobjective optimization problem that is solved by a hybrid of an evolutionary strategy and the quasi-Newton method. The choice of the transformation function is flexible and could be any continuous space function. We experiment with a linear and a nonlinear transformation in this paper. We show that the algorithm can outperform eight other classification methods, namely naive Bayes, support vector machines, linear discriminant analysis, multilayer perceptrons, decision trees, and k -nearest neighbors, and two recently proposed classification methods, in 12 standard classification data sets. Our results show that the method is less sensitive to the imbalanced number of instances compared with these methods. We also show that ODD maintains its performance better than other classification methods in these data sets and hence offers a better generalization ability.

An approach to image registration is outlined based on a new stochastic differential equation optimization method. The proposed method requires the use of the numerical solution of a particular stochastic differential equation to determine the iterative update of the transformation variables. A comparison to Differential Evolution optimization was carried out to establish the rate of convergence and the quality of result, as measured by the number of cost function evaluations and the size of the standard deviation of the optimal variables. Experimental data shows that the new technique is robust in terms of computational speed and convergence. The method is validated on magnetic resonance and histology images of mouse brain.

Existing fractal methods of texture analysis rely on the fractal dimension of textures as a function of scale for their discrimination and classification. We propose a method which is based on the possible multiscaling/multifractality of textures. A stochastic model is suggested to represent this multiscaling behaviour. We demonstrate the value of the method on a number of similar data sets (hence quite difficult for their discrimination) from the high-resolution Brodatz album.

Feature extraction and pattern classification are two key components in a pattern recognition system. In our approach, each image is represented by a 2D Fourier descriptor which is translation-, rotation-, and scale-invariant. We define a new metric, named the Hellinger-Kakutani metric for measuring the distance between two Fourier descriptors for classification. This metric is filtration-invariant, hence can be used on noisy images. The method is applied to a set of 22 Chinese characters, which contains 7 subsets of similar characters. The rate of accurate recognition is then reported.

A technique is developed to construct a representation of planar objects undergoing a general affine transformation. The representation can be used to describe planar or nearly planar objects in a three-dimensional space, observed by a camera under arbitrary orientations. The technique is based upon object contours, parameterized by an affine invariant parameter and the dyadic wavelet transform. The role of the wavelet transform is the extraction of multiresolution affine invariant features from the affine invariant contour representation. A dissimilarity function is also developed and used to distinguish among different object representations. This function makes use of the extrema on the representations, thus making its computation very efficient. A study of the effect of using different wavelet functions and their order or vanishing moments is also carried out. Experimental results show that the performance of the proposed representation is better than that of other existing methods, particularly when objects are heavily corrupted with noise.

A new algorithm to recognize a two-dimensional object of arbitrary shape is presented. The object boundary is first represented by a one-dimensional signal. This signal is then used to build the wavelet transform zero-crossing representation of the object. The algorithm is invariant to translation, rotation and scaling. Experimental results show that, compared with the use of Fourier descriptors, our algorithm gives more stable and accurate results.

A wavelet based representation of planar objects is introduced. Based on this representation, a matching algorithm using indexing techniques is also developed for identifying unknown objects. Rather than considering all points on the representation, only extrema are used in constructing the look-up table and for matching. Simulations demonstrate that the proposed algorithm is effective and accurate in classifying objects under similarity transformations and in a noisy environment.

A technique for representing and recognising 3-D or space curves is presented. In the proposed algorithm, the space curves are represented by a set of two zero-crossing representations which are constructed based on the dyadic wavelet transform. These representations are then described in the form of an ordered set of complex numbers which is referred to as the compact representation of the space curves. A string-matching technique is adapted for comparing two curves using their compact representations. Experimental results show that the proposed technique can be used for recognising space curves under similarity transformation with and without additive noise.

An algorithm for recognising space curves is introduced. The algorithm includes two stages : construction of space curve representation and a matching procedure. The representation is based on a dyadic wavelet transform. A dissimilarity function is defined and used in the matching procedure. Experimental results show that for 3D objects that can be represented by space curves, this algorithm is robust and efficient in extracting and matching object information.>

An algorithm based on the dyadic wavelet transform and complex Daubechies wavelets to recognise a planar object undergoing a general affine transformation is presented. The affine transformation most appropriately represents shape distortions arising from observing an object by a camera under arbitrary orientations. The proposed algorithm includes two steps: constructing the representation and the matching process. Experimental results show that the representation is robust and combined with the matching algorithm, it efficiently classifies unknown objects.>