Zhuhan Jiang

Similarity Enrichment in Image Compression through Weighted Finite Automata

We propose and study in details a similarity enrichment scheme for the application to the image compression through the extension of the weighted finite automata (WFA). We then develop a mechanism with which rich families of legitimate similarity images can be systematically created so as to reduce the overall WFA size, leading to an eventual better WFA-based compression performance. A number of desirable properties, including WFA of minimum states, have been established for a class of packed WFA. Moreover, a codec based on a special extended WFA is implemented to exemplify explicitly the performance gain due to extended WFA under otherwise the same conditions.

Tracking Camouflaged Objects with Weighted Region Consolidation

We propose an iterative method of Weighted Region Consolidation to track a camouflaged object within a background of very close colour in an image sequence, where the colours for both the object and the background are unsteady with large noises. More precisely, we will first detect the object motion based on both spatial and intensity densities by locating pixels with high motion probabilities from the difference data of successive frames. We then enhance the moving object iteratively, i.e. to consolidate the object region, by evaluating for each pixel its weighted overall neighbourhood intensity based on the pixel distances and intensity. The contour of the object’s moving area is then constructed, with an additional iterative process to refine the contour of the object in the current frame. We also propose to further refine the object contour, if needed, by the consideration of the neighbourhood intensities and shape similarity, the propagation of the initial contour, as well as the incorporation with other scattered and sketchy object boundaries obtained by another modified weight-based method applied on the edge map. Our proposed tracking scheme should be able to be eventually applied to monitoring the behavior of camouflaged wild life for their protection.

Lie symmetries and their local determinacy for a class of differential-difference equations

Abstract Differential-difference equations (DDEs) u n ( k ) ( t ) = F n ( t , u n + a ,…, u n + b ) for k ≥ 2 are studied for their differential Lie symmetries. We observe that while nonintrinsic Lie symmetries do exist in such DDEs, a great many admit only the intrinsic ones. We also propose a mechanism for automating symmetry calculations for fairly general DDEs, with a variety of features exemplified. In particular, the Fermi-Pasta-Ulam system is studied in detail and its new similarity solutions given explicitly.

Combined partial-bar and Riemann-Hilbert inverse methods for integrable non-linear evolution equations in (2+1) dimensions

The authors give a natural combination of partial-bar and Riemann-Hilbert problem inverse methods for an n th-order scalar spectral problem which solves a number of integrable non-linear evolution equations in two space and one time (2+1) dimensions. The theory embraces the two Kadomtsev-Petviashvili equations (1970) and their lump solutions.

Construction of scattering data for a class of multidimensional scattering operators

A systematic construction of the scattering data, and hence the inverse scattering transforms, is developed for a class of multidimensional matrix operators. The analysis embraces many of those for the widely scattering operators related to physically important equations. The paralleling methods when the space variables are partly or completely discretised are also given and discussed briefly.

Unification and extension of weighted finite automata applicable to image compression

Weighted finite automata (WFA), including the linear WFA due to Culik and Kari and the acyclic WFA due to Hafner, have been under investigation over the years for their applications to image compression. We shall in this work first examine in great details the underlying WFA structure and propose the most systematic extension, along with its full legitimacy analysis, to the WFA that are applicable to image compression. A new mechanism based on the concept of resolution-wise and resolution-driven image mappings is developed to create rich families of legitimate similarity images so as to reduce the overall WFA size, a property that is critically related the performance of WFA-based compression codecs. Moreover, we shall also unify the relevant WFA by showing an acyclic WFA can always be merged into a linear WFA but not vice versa.

Integrable multiwave interaction systems of ODEs

Abstract We prove complete integrability of a system of ODEs, the so called multiple 3-wave interaction equations, which are only loosely related to the 3-wave PDEs. We introduce an alternative nondegenerate matrix Lax representation which yields all the integrals of motion directly. A new general class of multiwave interaction ODEs is constructed and complete integrability proved for a nontrivial example of these.

An energy-conserved solitonic cellular automaton

An energy-conserved soliton cellular automaton is proposed. It is a generalization of the Park, Steiglitz and Thurston model (1986), and is shown to contain richer solitonic phenomena. A systematic comparison of their collision statistics is also given.

Integrable dynamical systems with quadratic and cubic nonlinearities related to graded Lie algebras

Practical implementation of two important methods of constructing integrable dynamical systems, the Lax pair method and the Adler–Konstant–Symes theorem, is studied. General considerations are illustrated by several examples that contain multiwave interaction systems and interacting Garnier systems as particular cases.

The ZS-AKNS inverse scattering transform with poles of multiple orders

Abstract The classical ZS-AKNS inverse method is generalised to include in a natural way poles of arbitrary orders in the transmission coefficient a ( z ) -1 , without imposing meromorphicity on the reflection coefficients. Compact forms of the generalised soliton solutions associated with single poles of arbitrary order n are also given together with simple examples.