We construct liftings of reduction maps from CM points to supersingular points for general quaternion algebras and use these liftings to establish a precise correspondence between CM points on indefinite quaternion algebras with a given conductor and CM points on certain corresponding totally definite quaternion algebras.

The research is Supported by Chongqing University postgraduates’ Science and Innovation Fund (200801A 1 A0070266). Abstract The purpose of this paper is to discuss the inequalities for the trace of self-conjugate quaternion matrix. We present the inequality for eigenvalues and trace of self-conjugate quaternion matrices. Based on the inequality above, we obtain several inequalities for the trac...

Pattern recognition techniques have been used to automatically recognize the objects, personal identities, predict the function of protein, the category of the cancer, identify lesion, perform product inspection, and so on. In this paper we propose a novel quaternion-based discriminant method. This method represents and classifies color images in a simple and mathematically tractable way. The p...

Estimating the structure of the human face is a long studied and difficult task. In this paper we present a new method for estimating facial structure from only a minimal number of salient feature points across a video sequence. The presented method uses both an Extended Kalman Filter (EKF) and a Kalman Filter (KF) to regress 3D Morphable Model (3DMM) shape parameters and solve 3D pose using a ...

We describe a model-based object tracking system that updates the connguration parameters of an object model based upon information gathered from a sequence of monocular images. Realistic object and imaging models are used to determine the expected visibility of object features, and to determine the expected appearance of all visible features. We formulate the tracking problem as one of paramet...

The Extended Kalman Filter (EKF) can be used for parameter as well as for state estimation. However, when used for parameter estimation, EKF is sensitive to modeling uncertainties and prone to instability. In this paper, the Variable Structure filtering concept is introduced and used for modifying the EKF into a robust form. The proposed method is model-based and has a guaranteed stability give...

Abstr~tct. Two new techniques have been developed to extract circles in computer images and this paper clarifies their implementation. One technique uses nonlinear least squares, the other an extended Kalman filter. Parameter estimation is based on analysing the residual gradient direction where the locus of an approximation to a circle intersects the target circle. This approach allows powerfu...

The unit quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Often, quaternion-based feedback control laws require an additional mechanism that lifts a continuous attitude trajectory to the unit quaternion space. Lifting mechanisms that are memoryless, for example, selecting the quaternion having positive scalar component, h...

We describe a model-based object tracking system that updates the configuration parameters of an object model based upon information gathered from a sequence of monocular images. Realistic object and imaging models are used to determine the expected visibility of object features, and to determine the expected appearance of all visible features. We formulate the tracking problem as one of parame...