Real time pattern recognition applications often deal with high dimensional data, which require a data reduction step which is only performed offline. However, this loses the possibility of adaption to a changing environment. This is also true for other applications different from pattern recognition, like data visualization for input inspection. Only linear projections, like the principal component analysis, can work in real time by using iterative algorithms while all known nonlinear techniques cannot be implemented in such a way and actually always work on the whole database at each epoch. Among these nonlinear tools, the Curvilinear Component Analysis (CCA), which is a non-convex technique based on the preservation of the local distances into the lower dimensional space, plays an important role. This paper presents the online version of CCA. It inherits the same features of CCA, is adaptive in real time and tracks non-stationary high dimensional distributions. It is composed of neurons with two weights: one, pointing to the input space, quantizes the data distribution, and the other, pointing to the output space, represents the projection of the first weight. This on-line CCA has been conceived not only for the previously cited applications, but also as a basic tool for more complex supervised neural networks for modelling very complex high dimensional data. This algorithm is tested on 2-D and 3-D synthetic data and on an experimental database concerning the bearing faults of an electrical motor, with the goal of novelty (fault) detection.

We present a computationally efficient demosaicing algorithm based on a luminance-chrominance model of the color filter array (CFA) image. We show that the chrominance information can be estimated using simple low-pass filtering. This algorithm allows us to use separable recursive filters, which are particularly adapted for real-time processing. Moreover, while most of demosaicing algorithms are specific to a particular CFA (usually the popular Bayer CFA), our method can be applied to any CFA. We present a linear version of the algorithm and an adaptive extension.

There is an analogy between single-chip color cameras and the human visual system in that these two systems acquire only one limited wavelength sensitivity band per spatial location. We have exploited this analogy, defining a model that characterizes a one-color per spatial position image as a coding into luminance and chrominance of the corresponding three colors per spatial position image. Luminance is defined with full spatial resolution while chrominance contains subsampled opponent colors. Moreover, luminance and chrominance follow a particular arrangement in the Fourier domain, allowing for demosaicing by spatial frequency filtering. This model shows that visual artifacts after demosaicing are due to aliasing between luminance and chrominance and could be solved using a preprocessing filter. This approach also gives new insights for the representation of single-color per spatial location images and enables formal and controllable procedures to design demosaicing algorithms that perform well compared to concurrent approaches, as demonstrated by experiments.

The minor component analysis (MCA) deals with the recovery of the eigenvector associated to the smallest eigenvalue of the autocorrelation matrix of the input data and is a very important tool for signal processing and data analysis. It is almost exclusively solved by linear neurons. This paper presents a linear neuron endowed with a novel learning law, called MCA EXINn and analyzes its features. The neural literature about MCA is very poor, in the sense that both a little theoretical basis is given (almost always focusing on the ODE asymptotic approximation) and only experiments on toy problems (at most four-dimensional problems) are presented, without any numerical analysis. This work addresses these problems and lays sound theoretical foundations for the neural MCA theory. In particular, it classifies the MCA neurons according to the Riemannian metric and justifies, from the analysis of the degeneracy of the error cost; the different behavior in approaching convergence. The cost landscape is studied and used as a basis for the analysis of the asymptotic behavior. All the phases of the dynamics of the MCA algorithms are investigated in detail and, together with the numerical analysis, lead to the identification of three possible kinds of divergence, here called sudden, dynamic, and numerical. The importance of the choice of low initial conditions is also explained. A lot of importance is given to the experimental part, where simulations on high-dimensional problems are,presented and analyzed. The orthogonal regression or total least squares (TLS) technique is also presented, together with a real-world application on the identification of the parameters of an electrical machine. It can be concluded that MCA EXIN is the best MCA neuron in terms of stability (no finite time divergence), speed, and accuracy.

Natural image retrieval is a main challenge for image indexing. In this domain, colour information is one of the most important features. We propose a perceptive colour space based on a biological model of the retina. In this space, a model of Gaussian mixture appears very efficient for colour distribution. Two strategies are presented, retrieval by maximum likelihood (i) on the global chromatic distribution, (ii) on the local spatio-chromatic distribution.

We present a new strategy called "curvilinear component analysis" (CCA) for dimensionality reduction and representation of multidimensional data sets. The principle of CCA is a self-organized neural network performing two tasks: vector quantization (VQ) of the submanifold in the data set (input space); and nonlinear projection (P) of these quantizing vectors toward an output space, providing a revealing unfolding of the submanifold. After learning, the network has the ability to continuously map any new point from one space into another: forward mapping of new points in the input space, or backward mapping of an arbitrary position in the output space.