Real time feature-based facial tracking using Lie algebras

We have developed a novel human facial tracking system that operates in real time at a video frame rate without needing any special hardware. The approach is based on the use of Lie algebra, and uses three-dimensional feature points on the targeted human face. It is assumed that the roughly estimated facial model (relative coordinates of the three-dimensional feature points) is known. First, the initial feature positions of the face are determined using a model fitting technique. Then, the tracking is operated by the following sequence: (1) capture the new video frame and render feature points to the image plane; (2) search for new positions of the feature points on the image plane; (3) get the Euclidean matrix from the moving vector and the three-dimensional information for the points; and (4) rotate and translate the feature points by using the Euclidean matrix, and render the new points on the image plane. The key algorithm of this tracker is to estimate the Euclidean matrix by using a least square technique based on Lie algebra. The resulting tracker performed very well on the task of tracking a human face.

响蜜lie科的新记录

报道并简述了1994年10月在云南省泸水县的老窝捕获到1只响蜜lie科的黄腰响蜜lieIndicator xanthonotus 为我国鸟类科的新记录。模式标本保存于作者单位。

Coordinated motion design on lie groups

The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics. It thereby shows that coordination can be studied in a systematic way once the Lie group geometry of the configuration space is well characterized. Applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds. A link with Brockett's double bracket flows is also made. The concepts are illustrated on SO(3), SE(2) and SE(3). © 2010 IEEE.

Coordination on Lie groups

This paper studies the coordinated motion of a group of agents evolving on a Lie group. Left-or rightinvariance with respect to the absolute position on the group lead to two different characterizations of relative positions and two associated definitions of coordination (fixed relative positions). Conditions for each type of coordination are derived in the associated Lie algebra. This allows to formulate the coordination problem on Lie groups as consensus in a vector space. Total coordination occurs when both types of coordination hold simultaneously. The discussion in this paper provides a common geometric framework for previously published coordination control laws on SO(3), SE(2) and SE(3). The theory is illustrated on the group of planar rigid motion SE(2). © 2008 IEEE.

Optimal data fitting on lie groups: A coset approach

This work considers the problem of fitting data on a Lie group by a coset of a compact subgroup. This problem can be seen as an extension of the problem of fitting affine subspaces in n to data which can be solved using principal component analysis. We show how the fitting problem can be reduced for biinvariant distances to a generalized mean calculation on an homogeneous space. For biinvariant Riemannian distances we provide an algorithm based on the Karcher mean gradient algorithm. We illustrate our approach by some examples on SO(n). © 2010 Springer -Verlag Berlin Heidelberg.

On a new genus and new species of xanthid crab (Crustacea, Decapoda, Brachyura, Xanthinae) from the South China Sea, with notes on the genus Liagore De Haan, 1833

A new genus and new species of xanthid crab, Ovatis simplex, is described from the South China Sea. The genus is closest to Liagore but can be distinguished by a suite of carapace and male gonopod characters. The systematic position of Liagore is also considered, and both genera, Liagore and Ovatis, are here referred to the subfamily Xanthinae. Comparisons with the allied genera, Paratergatis and Pulcratis, are also provided.

Application of dynamical Lie algebraic method to atom-diatomic molecule scattering

The dynamical Lie algebraic approach developed by Alhassid and Levine combined with intermediate picture is applied to the study of translational-vibrational energy transfer in the collinear collision between an atom and an anharmonic oscillator. We find that the presence of the anharmonic terms indeed has an effect on the vibrational probabilities of the oscillator. The computed probabilities are in good agreement with those obtained using exact quantum method. It is shown that the approach of dynamical Lie algebra combining with intermediate picture is reasonable in the treating of atom-anharmonic oscillator scattering.

THE PIANO MUSIC OF ROBERT SCHUMANN (1810-1856) AND JOHANNES BRAHMS (1833- 1897): A SURVEY OF CONCERTI, VARIATIONS, AND CHARACTER PIECES

Robert Schumann (1810-1856) and Johannes Brahms (1833-1897), in some ways Robert Schumann's artistic descendant, are the most important and representative German piano composers during the Romantic period. Schumann was already a mature and established musician in 1853 when he first met the young Brahms and recognized his talents, an encounter that had a long-lasting affect on the lives and careers of both men. After Schumann’s mental breakdown and death, Brahms maintained his admiration of Schumann’s music and preserved an intimate relationship with Clara Schumann. In spite of the personal and musical closeness of the two men, Schumann’s music is stylistically distinct from that of Brahms. Brahms followed traditions from Baroque and Classical music, and avoided using images and expressive titles in his music. Brahms extraordinarily intermingled earlier musical forms with multicolored tones of German Romanticism. In contrast, Schumann saw himself as a radical composer devoted to personal emotionalism and spontaneity. He favored programmatic titles for his character pieces and extra-musical references in his music. While developing their own musical styles as German Romantic composers, Schumann and Brahms both utilized the piano as a resourceful tool for self-realization and compositional development. To investigate and compare the main characteristics of Schumann and Brahms’s piano music, I looked at three genres. First, in the category of the piano concerto, I chose two major Romantic works, Schumann’s A minor concerto and Brahms’s B-flat major concerto. Second, for the category of piano variations I included two sets by Brahms because the variation framework was such an important vehicle for him to express his musical thoughts. Schumann’s unique motivic approach to variation is displayed vividly in his character-piece cycle Carnaval. Third, the category of the character piece, perhaps the favorite medium of Romantic expression at the piano, is shown by Schumann’s Papillons and Brahms’s sets of pieces Op.118 and Op.119. This performance dissertation consists of three recitals performed in the Gildenhorn Recital Hall at the University of Maryland, College Park. These recitals are documented on compact disc recordings that are housed within the University of Maryland Library System.

SELECTED CHARACTER PIECES OF FRÉDÉRIC CHOPIN (1810-1849), FRANZ LISZT (1811-1886) AND JOHANNES BRAHMS (1833-1897)

During the 19th century, Frédéric Chopin (1810-1849), Franz Liszt (1811- 1886), and Johannes Brahms (1833-1897) were among the most recognized composers of character pieces. Their compositions have been considered a significant milestone in piano literature. Frédéric Chopin (1810-1849) did not give descriptive titles to his character pieces. He grouped them into several genres such as Mazurkas, Polonaises. His Mazurkas and Polonaises are influenced by Polish dance music and inspired by the polish national idiom. Franz Liszt (1811-1886) was influenced in many ways by Chopin, and adopted Chopin’s lyricism, melodic style, and tempo rubato. However, Liszt frequently drew on non-musical subjects (e.g., art, literature) for inspiration. “Harmonies poétiques et religieuses” and “Années de pèlerinage” are especially representative of character pieces in which poetic and pictorial imagination are reflected. Johannes Brahms (1833-1897) was a conservative traditionalist, synthesizing Romantic expression and Classical tradition remarkably well. Like Chopin, Brahms avoided using programmatic titles for his works. The titles of Brahms’ short character pieces are often taken from traditional lyrical or dramatic genres such as ballade, rhapsody and scherzo. Because of his conservatism, Brahms was considered the main rival of Liszt in the Romantic Period. Brahms character pieces in his third period (e.g., Scherzo Op.4, Ballades of Op.10, and Rhapsodies of Op.79) are concise and focused. The form of Brahms’ character pieces is mostly simple ternary (ABA), and his style is introspective and lyrical. Through this recording project, I was able to get a better understanding of the styles of Chopin, Brahms and Liszt through their character pieces. This recording dissertation consists of two CDs recorded in the Dekelboum Concert Hall at the University of Maryland, College Park. These recordings are documented on compact disc recordings that are housed within the University of Maryland Library System.