Multidimensional projection techniques have experienced many improvements lately, mainly regarding computational times and accuracy. However, existing methods do not yet provide flexible enough mechanisms for visualization-oriented fully interactive applications. This work presents a new multidimensional projection technique designed to be more flexible and versatile than other methods. This novel approach, called Local Affine Multidimensional Projection (LAMP), relies on orthogonal mapping theory to build accurate local transformations that can be dynamically modified according to user knowledge. The accuracy, flexibility and computational efficiency of LAMP is confirmed by a comprehensive set of comparisons. LAMP's versatility is exploited in an application which seeks to correlate data that, in principle, has no connection as well as in visual exploration of textual documents.

In this work a variational model is proposed for simultaneous smoothing and multiphase image segmentation. By assuming that the pixel intensities are independent samples from a mixture of Gaussians, and by interpreting the phase fields as probabilities of pixels belonging to a certain phase, the model formulation is obtained by maximizing the mutual information between image features and phase fields. The proposed energy functional Jeconsists of three parts: the smoothing term for the reconstructed image, the regularization for the boundaries in hard segmentation, and a likelihood estimator based on the density function. The segmentation and image denoising are performed simultaneously through the flow equation obtained by minimizing the energy functional with respect to the mixture of Gaussian coefficients and variance. Some experimental results on segmenting synthetic and natural color images are presented to illustrate the effectiveness of the proposed model.