Karhunen Loève Transformation algorithm for automatic image registration

CESAR F. CAIAFA; ARACELI N. PROTO

La Serena, CHILE

Conferencia; MEDYFINOL'04 (XIV Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics; 2004

Universidad de los Andes

During last years many papers have appeared in the literature approaching the Image Registration problem, mainly focusing into Remote Sensing Applications and Medical Imaging. While classic techniques like Cross Correlation Coefficient calculation, Fourier Methods and others  are being used from long time ago, new techniques based on Mutual Information Maximization,  Spline Processing  and others has recently been introduced by many authors. The Registration Process is very important task in image analysis due to the fact that a precise registration is the critical prior step in most of the procedures that merge several images to construct a new image version with a significant improvement in  its quality .     In the present paper we introduce a new algorithm based on the Karhunen Loève Transformation (KLT) to approach the  automatic registration of satellite images, both for radar or optical images. Our method is based on the projection of the data under analysis onto an appropriate pair of orthogonal subspaces. These subspaces are obtained using the theory of the Karhunen-Loève transformation (KLT). We define important quantities related with the Mimum Mean Square Error as DFPS (Distance From Pattern Space),  DIPSj  (Distance In Pattern Space to Pattern j) previously used (Moghaddam, B.; Pentland, A, “Probabilistic visual learning for object detection”, Computer Vision, 1995) in a different context, and introduce a new one: the AFPS (Angle From Pattern Space). We compare the effectiveness of considering only Euclidean Distance versus a combination of Euclidean Distance and AFPS.  The processed images have been captured by the same satellite sensor (MERIS, Satellite Image - source: ESA European Space Agency) in two different days. The geographic area used in the registration process example is part of south of Portugal (taken from the ESA Image Galery: Lisbon, Portugal – MERIS, 8 March 2003 and Strait of Gibraltar - MERIS, 18 June 2003). We have presented a new approach to the Registration problem for satellite images based on KLT representation of vectorized data. We have demonstrated that the Euclidean Distance or MSE (Minimum Squared Error) in KLT basis, can be expressed as a decomposition  into two measures DFPS (Distance From Pattern Space) and DIPSj  (Distance In Pattern Space to Pattern j). This KLT decomposition of the Euclidean Distance allows us to acquire much more information about our pattern structure and therefore the resulting strategy has higher performance.   Besides, we introduce a new estimator, AFPS, and we have developed an algorithm to calculate AFPS, DFPS and DIPSj  for a sliding window based in FFT algorithm which give us a fast way to evaluate these important quantities as a function of the position of the window. Through these three quantities we design an automatic procedure for image registration.