We present a novel framework for the automatic discovery and recognition of motion primitives in videos of human activities. Given the 3D pose of a human in a video, human motion primitives are discovered by optimizing the motion flux', a quantity which captures the motion variation of a group of skelet al joints. A normalization of the primitives is proposed in order to make them invariant with respect to a subject anatomical variations and data sampling rate. The discovered primitives are unknown and unlabeled and are unsupervisedly collected into classes via a hierarchical non-parametric Bayes mixture model. Once classes are determined and labeled they are further analyzed for establishing models for recognizing discovered primitives. Each primitive model is defined by a set of learned parameters. Given new video data and given the estimated pose of the subject appearing on the video, the motion is segmented into primitives, which are recognized with a probability given according to the parameters of the learned models. Using our framework we build a publicly available dataset of human motion primitives, using sequences taken from well-known motion capture datasets. We expect that our framework, by providing an objective way for discovering and categorizing human motion, will be a useful tool in numerous research fields including video analysis, human inspired motion generation, learning by demonstration, intuitive human-robot interaction, and human behavior analysis.
Neurophysiology studies on motion primitives @cite_72 @cite_90 @cite_67 @cite_66 @cite_79 @cite_5 are based on the idea that kinetic energy and muscular activity are optimized in order to conserve energy. In these works it has been observed that curvature and velocity of joint motion are related. Earliest works such as @cite_14 proposed a relation between curvature and angular velocity. In particular, using their notation, letting @math be the curvature and @math the angular velocity, they called the equation @math the Two-Thirds Power law, valid for certain class of two-dimensional movements. Viviani and Schneider @cite_46 formulated an extension of this law, relating the radius of curvature @math at any point @math along the trajectory with the corresponding tangential velocity @math , in their notation:
@cite_67 @cite_14 @cite_90 @cite_79 @cite_72 @cite_5 @cite_46 @cite_66
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Humans interact with their environment through sensory information and motor actions. These interactions may be understood via the underlying geometry of both perception and action. While the motor space is typically considered by default to be Euclidean, persistent behavioral observations point to a different underlying geometric structure. These observed regularities include the “two-thirds power law”, which connects path curvature with velocity, and “local isochrony”, which prescribes the relation between movement time and its extent. Starting with these empirical observations, we have developed a mathematical framework based on differential geometry, Lie group theory and Cartan’s moving frame method for the analysis of human hand trajectories. We also use this method to identify possible motion primitives, i.e., elementary building blocks from which more complicated movements are constructed. We show that a natural geometric description of continuous repetitive hand trajectories is not Euclidean but equi-affine. Specifically, equi-affine velocity is piecewise constant along movement segments, and movement execution time for a given segment is proportional to its equi-affine arc-length. Using this mathematical framework, we then analyze experimentally recorded drawing movements. To examine movement segmentation and classification, the two fundamental equi-affine differential invariants—equi-affine arc-length and curvature are calculated for the recorded movements. We also discuss the possible role of conic sections, i.e., curves with constant equi-affine curvature, as motor primitives and focus in more detail on parabolas, the equi-affine geodesics. Finally, we explore possible schemes for the internal neural coding of motor commands by showing that the equi-affine framework is compatible with the common model of population coding of the hand velocity vector when combined with a simple assumption on its dynamics. We then discuss several alternative explanations for the role that the equi-affine metric may play in internal representations of motion perception and production. Considerable evidence exists that the velocity of execution of handwriting and drawing movements depends on some global metric properties of the movement (size, linear extent etc.). Recent experiments have demonstrated that the instantaneous velocity also depends on the local curvature of the trajectory, that is, on the differential geometrical properties of the movement. In this paper we investigate further the role of the differential factors. Experiments are described in which drawing movements of simple geometrical forms and scribbles are performed either freely and extemporaneously, or in the presence of external constraints. It is shown that, at any time during the movement, the velocity component related to differential factors only depends on the value of the curvature of the trajectory at the same time (no dynamics). The relation can be described quantitatively as a specific Power Law and applies to all movements considered here, including those which are performed by following the edge of a template. The fact that the velocity of execution increases with the radius of curvature implies a built-in tendency of the motor control system to keep angular velocity relatively constant and qualifies the Isogony Principle proposed previously. The specific exponent of the Power Law suggests a possible interpretation of this empirical relation. Abstract This article reports an experimental study that aimed to quantitatively analyze motion coordination patterns across digits 2–5 (index to little finger), and examine the kinematic synergies during manipulative and gestic acts. Twenty-eight subjects (14 males and 14 females) performed two types of tasks, both right-handed: (1) cylinder-grasping that involved concurrent voluntary flexion of digits 2–5, and (2) voluntary flexion of individual fingers from digit 2 to 5 (i.e., one at a time). A five-camera opto-electronic motion capture system measured trajectories of 21 miniature reflective markers strategically placed on the dorsal surface landmarks of the hand. Joint angular profiles for 12 involved flexion–extension degrees of freedom (DOF's) were derived from the measured coordinates of surface markers. Principal components analysis (PCA) was used to examine the temporal covariation between joint angles. A mathematical modeling procedure, based on hyperbolic tangent functions, characterized the sigmoidal shaped angular profiles with four kinematically meaningful parameters. The PCA results showed that for all the movement trials ( n =280), two principal components accounted for at least 98 of the variance. The angular profiles ( n =2464) were accurately characterized, with the mean (±SD) coefficient of determination ( R 2 ) and root-mean-square-error (RMSE) being 0.95 (±0.12) and 1.03° (±0.82°), respectively. The resulting parameters which quantified both the spatial and temporal aspects of angular profiles revealed stereotypical patterns including a predominant (87 of all trials) proximal-to-distal flexion sequence and characteristic interdependence – involuntary joint flexion induced by the voluntarily flexed joint. The principal components' weights and the kinematic parameters also exhibited qualitatively similar variation patterns. Motor control interpretations and new insights regarding the underlying synergistic mechanisms, particularly in relation to previous findings on force synergies, are discussed. Trajectory and kinematics of drawing movements are mutually constrained by functional relationships that reduce the degrees of freedom of the hand-arm system. Previous investigations of these relationships are extended here by considering their development in children between 5 and 12 years of age. Performances in a simple motor task—the continuous tracing of elliptic trajectories—demonstrate that both the phenomenon of isochrony (increase of the average movement velocity with the linear extent of the trajectory) and the so-called two-thirds power law (relation between tangential velocity and curvature) are qualitatively present already at the age of 5. The quantitative aspects of these regularities evolve with age, however, and steady-state adult performance is not attained even by the oldest children. The power-law formalism developed in previous reports is generalized to encompass these developmental aspects of the control of movement. Two general frameworks are currently available to conceptualize the motor-control problem. Broadly, the two frameworks differ in the answer that they give to the question "Where do form and structure come from?" According to the motor-program view (e.g., Schmidt, 1988), form and structure in a movement come from a central abstract representation of the intended result. Thus, making a movement entails a detailed mapping of this representation into an appropriate motor plan. The competing task-dynamic view (e.g., Kugler, 1989; Saltzman & Kelso, 1987) emphasizes instead the global morphogenetic power of the nonlinearities of the motor system. These two views need not be mutually exclusive. In fact, different classes of movements may require different conceptual frameworks for their analysis. At any rate (at least in the case of drawing movements considered here), an internal representation of the intended trajectory and kinematics must be available before execution. Consequently, much effort is being devoted to understanding how this internal model is translated into a set of motor commands. In this respect, one basic conceptual difficulty is because the geometry of the arm-forearm-hand system affords a large number of degrees of freedom. Provided that there are no constraints in the workspace, the only trajectory that matters in many manual