Textons refer to fundamental micro-structures in generic natural images and thus constitute the basic elements in early (pre-attentive) visual perception. However, the word textong remains a vague concept in the literature of computer vision and visual perception, and a precist mathematical definition has yet to be found. In this article, we argue that the definition of texton should be governed by a sound mathematical model of images, and the set of textons must be learned from, or best tuned to, an image ensemble. We adopt a generative image model that an image is a superposition of bases from an over-complete dictionary, then a texton is defined as a mini-template that consists of a varying number of image bases with some geometric and photometric configurations. By analogy to physics, if image bases are like protons, neutrons and electrons, then textons are like atoms. Then a small number of textons can be learned from training images as repeating micro-structures. We report four experiments for comparison. The first experiment computes clusters in feature space of filter responses. The second transformed component analysis in both feature space and image patches. The third adopts a two-layer generative model where an image is generated by image bases and image bases are generated by textons. The fourth experiment shows textons from motion image sequences, which we call movetons.

What are Textons

Markov switching models MSMs are probabilistic models that employmultiple sets of parameters to describe different dynamic regimesthat a time series may exhibit at different periods of time. Theswitching mechanism between regimes is controlled by unobserved randomvariables that form a first-order Markov chain. Explicit-durationMSMs contain additional variables that explicitly model the distributionof time spent in each regime. This allows to define duration distributionsof any form, but also to impose complex dependence betweenthe observations and to reset the dynamics to initial conditions. Modelsthat focus on the first two properties are most commonly known as hiddensemi-Markov models or segment models, whilst models that focuson the third property are most commonly known as changepoint modelsor reset models. In this monograph, we provide a description of explicitdurationmodelling by categorizing the different approaches into threegroups, which differ in encoding in the explicit-duration variables differentinformation about regime change/reset boundaries. The approachesare described using the formalism of graphical models, which allows tographically represent and assess statistical dependence and thereforeto easily describe the structure of complex models and derive inferenceroutines. The presentation is intended to be pedagogical, focusingon providing a characterization of the three groups in terms of modelstructure constraints and inference properties. The monograph is supplementedwith a software package that contains most of the modelsand examples described. The material presented should be useful toboth researchers wishing to learn about these models and researcherswishing to develop them further.The supplementary data for this issue will be available soon.

/pdf/explicit-duration-markov-switching-models-22r4w91q3u.pdf

Explicit-Duration Markov Switching Models

In this paper, we propose a constrained least squares approach for stably computing Laplacian deformation with strict positional constraints. In the existing work on Laplacian deformation, strict positional constraints are described using large values of least squares weights, which often cause numerical problems when Laplacians are described using cotangent weights. In our method, we describe strict positional constraints as hard constraints. We solve the combination of hard and soft constraints by constructing a typical least squares matrix form using QR decomposition. In addition, our method can manage shape deformation under over-constraints, such as redundant and conflicting constraints. Our framework achieves excellent performance for interactive deformation of mesh models.

A Constrained Least Squares Approach to Interactive Mesh Deformation.

Aspects of the present invention include systems and methods for segmentation and recognition of action primitives. In embodiments, a framework, referred to as the Continuous Linear Dynamic System (CLDS), comprises two sets of Linear Dynamic System (LDS) models, one to model the dynamics of individual primitive actions and the other to model the transitions between actions. In embodiments, the inference process estimates the best decomposition of the whole sequence into continuous alternating between the two set of models, using an approximate Viterbi algorithm. In this way, both action type and action boundary may be accurately recognized.

Continuous linear dynamic systems

A joint-based hierarchical analysis model of human motion was proposed to solve the problem of the movement intent and quantitative description in human body postures. In this paper, a statistical observation was made on about 181 h video data to be summarized as 31 basic activities, which are defined by genera and species. A four-level hierarchical model with posture- activity- motion- style was proposed in this paper, which is specified formally by PDM (Point Distribution Models). At the final, the model validations were given by the experiments and applications.

Hierarchical Analysis Model of Human Motion

Statistical model is an effective method for character motion modeling. In this paper, a variable duration motion texture is proposed to represent complex human motion that is statistically similar to the original captured motion data. The motion texture is defined as a three-level structure with moton abstracts, motons and their distribution. The motion texture is modeled by a Semi-SLDS (Semi- Switching Linear Dynamic System), which provides an intuitive framework for describing the continuous but nonlinear dynamics of human motion. To explicitly incorporate duration modeling capability, the Semi-SLDS is adopted to improve SLDS by replacing the Markov switching layer with semi-Markov model. In addition, the proposed approach is proved flexible and effective by several motion applications, namely motion synthesis, motion recognition and motion compression.

Variable duration motion texture for human motion modeling

Statistical model is an effective method for character motion modeling. In this paper, a variable duration motion texture is proposed to represent complex human motion that is statistically similar to the original captured motion data. The motion texture is defined as a threelevel structure with moton abstracts, motons and their distribution. The motion texture is modeled by a Semi-SLDS (Semi- Switching Linear Dynamic System), which provides an intuitive framework for describing the continuous but nonlinear dynamics of human motion. To explicitly incorporate duration modeling capability, the Semi-SLDS is adopted to improve SLDS by replacing the Markov switching layer with semi-Markov model. In addition, the proposed approach is proved flexible and effective by several motion applications, namely motion synthesis, motion recognition and motion compression.

A three-level motion texture is proposed to model complex human motion that is statistically similar to the original motion data. The three-level structure, namely moton index, moton and moton distribution, is defined to synthesize motions. To describe the continuous and non-linear dynamics of human motion, the motion texture is modeled by a Non-Stationary Switching Linear Dynamic System (NS-SLDS), which improves the Switching Linear Dynamic System (SLDS) by non-stationary functions. A BSK-tree (Binary Key-pose Splitting Tree) retrieval method applied in motons supplies the ability to access data in frame-level. Thus the motion texture can be manipulated at three different levels, by retrieving key-frame in specific moton, by changing the details of a specific motion at the moton-level and by designing a new choreography at the distribution-level. In motion synthesis experiments, the proposed approach was proved flexible and effective.

A Three-level Motion Texture for Human Motion Modeling

This paper proposes a novel hardware-accelerating deformation algorithm based on curve-skeleton model for 2D shape manipulation. The deformation algorithm can achieve real-time interactive shape manipulation without any pre-computing step. The deforming regions of shapes are demarcated with a simple skeleton frame and are simulated by a curve-skeleton model consisting of triangle-strips. The algorithm obtains two properties that smooth flexion and preservation of area. Smooth flexion is guaranteed due to the continuous derivative of the curve function, and preservation of area is achieved via adjusting the parameters of the control curves. GPGPU technique is adopted to reduce the workload on CPU and to accelerate the rendering. Our algorithm can be used to 2D shape manipulation, character animation and cartoon-like objects deformation. It has been proved feasible and valid by our experiments.

Shape Manipulation on GPU

In this paper, we present a novel system for simultaneously performing segmentation and 2D pose motion recovery for
the articulated object in a video sequence. The system first preprocesses pixels into superpixels to reduce the number of
nodes which largely affects the computational complexity of later optimizations. By starting from true pose estimation
obtained with user assistants on each key frame, a parallel pose tracking procedure, whose energy function considers
boundary, appearance and pose prior information as well, is conducted forward and backward on in-between frames.
With different searching strategies, multiple pose candidates are inferred to help recover missed true poses. Finally, by
solving the cost function of the pose motion recovery, which exploits the temporal coherence of object movement, the
pose motion and the video object are produced at the mean time. As a parameterized tree-based articulated model drawn
by the user is applied to denote the pose, our method is generic and can be used for any articulated object.

Simultaneous pose motion recovery and video object cutout

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Variable duration motion texture for human motion modeling

Variable duration motion texture for human motion modeling

A Three-level Motion Texture for Human Motion Modeling

Shape Manipulation on GPU

Simultaneous pose motion recovery and video object cutout