Recent work on anatomical face modeling focuses mainly on facial muscles and their activation. This paper considers a different aspect of anatomical face modeling: kinematic modeling of the jaw, i.e., the temporomandibular joint (TMJ). Previous work often relies on simple models of jaw kinematics, even though the actual physiological behavior of the TMJ is quite complex, allowing not only for mouth opening, but also for some amount of sideways (lateral) and front-to-back (protrusion) motions. Fortuitously, the TMJ is the only joint whose kinematics can be accurately measured with optical methods, because the bones of the lower and upper jaw are rigidly connected to the lower and upper teeth. We construct a person-specific jaw kinematic model by asking an actor to exercise the entire range of motion of the jaw while keeping the lips open so that the teeth are at least partially visible. This performance is recorded with three calibrated cameras. We obtain highly accurate 3D models of the teeth with a standard dental scanner and use these models to reconstruct the rigid body trajectories of the teeth from the videos (markerless tracking). The relative rigid transformations samples between the lower and upper teeth are mapped to the Lie algebra of rigid body motions in order to linearize the rotational motion. Our main contribution is to fit these samples with a three-dimensional nonlinear model parameterizing the entire range of motion of the TMJ. We show that standard principal component analysis (PCA) fails to capture the nonlinear trajectories of the moving mandible. However, we found these nonlinearities can be captured with a special modification of autoencoder neural networks known as nonlinear PCA. By mapping back to the Lie group of rigid transformations, we obtain a parametrization of the jaw kinematics which provides an intuitive interface allowing the animators to explore realistic jaw motions in a user-friendly way.
The need for jaw kinematic modeling was identified in previous work in computer graphics. @cite_1 created a jaw kinematics rig by designing sliding tracks of the condyles identified from magnetic resonance images. Because MRI is not always available and may be even medically contraindicated, @cite_3 proposed a geometric rig offering two rotational degrees of freedom along a common pivot point and one translational degree of freedom along a fixed axis. This model was slightly generalized by @cite_28 who proposed using three translational degrees of freedom instead of just one, in addition to the two original rotational degrees of freedom. @cite_11 use an articulated model including the neck and eyeballs, with three rotational degrees of freedom for each of the joints, including the jaw. Our approach does not require MRI but still produces highly accurate data-driven jaw kinematics model for a given actor.
@cite_28 @cite_1 @cite_3 @cite_11
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Abstract Mandibular distraction osteogenesis will lead to a change in muscle coordination and load transfer to the temporomandibular joints (TMJ). The objective of this work is to present and validate a rigid-body musculo-skelet al model of the mandible based on inverse dynamics for calculation of the muscle activations, muscle forces and TMJ reaction forces for different types of clenching tasks and dynamic tasks. This approach is validated on a symmetric mandible model and an application will be presented where the TMJ reaction forces during unilateral clenching are estimated for a virtual distraction patient with a shortened left ramus. The mandible model consists of 2 rigid segments and has 4 degrees-of-freedom. The model was equipped with 24 hill-type musculotendon actuators. During the validation experiment one subject was asked to do several tasks while measuring EMG activity, bite force and kinematics. The bite force and kinematics were used as input for the simulations of the same tasks after which the estimated muscle activities were compared with the measured muscle activities. This resulted in an average correlation coefficient of 0.580 and an average of the Mean Absolute Error of 0.109. The virtual distraction model showed a large difference in the TMJ reaction forces between left and right compared with the symmetric model for the same loading case. The present work is a step in the direction of building patient-specific mandible models, which can assess the mechanical effects on the TMJ before mandibular distraction osteogenesis surgery. Statement of problem Composite mandibular resection resulting in mandibular discontinuity can alter jaw motion, occlusal forces, and mastication, whether or not the jaw is reconstructed. The biomechanical events associated with these changes are difficult to assess clinically and, therefore, are not well documented or researched. Purpose The purpose of this study was to model movements of a mandible with a discontinuity defect, and to compare them to movements of a mandible with its continuity restored by alloplastic reconstruction. Material and methods Computational models were created with a novel simulation platform. The variables designed into the models included gravity, external forces, and jaw muscle activity. Each jaw was observed at rest, when opened by external force or by muscle drive, and during the generation of unilateral occlusal force on the nonoperated side. Scarring was simulated with springlike forces. Outputs included individual muscle forces and torques, as well as mandibular incisor and condylar motions. Results Both models displayed plausible resting postures, and jaw opening with deviation toward the defect side when scarring was simulated. Opening caused by downward force on the incisors differed from that due to muscle activation. Jaw rotations during unilateral molar contact on the unaffected side were muscle specific and influenced by mandibular discontinuity. Conclusions Plausible jaw movements after hemimandibulectomy and or alloplastic reconstruction could be predicted by dynamic modeling. The effect of soft tissue forces on jaw posture and movements varied with the condylar support available. In both models, different opening trajectories were produced by external force on the jaw and by jaw muscle activation. Mandibular rotation during unilateral molar contact depended on which muscles were activated, and the availability of bilateral condylar support. We present a novel method for accurate marker-less capture of articulated skeleton motion of several subjects in general scenes, indoors and outdoors, even from input filmed with as few as two cameras. Our approach unites a discriminative image-based joint detection method with a model-based generative motion tracking algorithm through a combined pose optimization energy. The discriminative part-based pose detection method, implemented using Convolutional Networks (ConvNet), estimates unary potentials for each joint of a kinematic skeleton model. These unary potentials are used to probabilistically extract pose constraints for tracking by using weighted sampling from a pose posterior guided by the model. In the final energy, these constraints are combined with an appearance-based model-to-image similarity term. Poses can be computed very efficiently using iterative local optimization, as ConvNet detection is fast, and our formulation yields a combined pose estimation energy with analytic derivatives. In combination, this enables to track full articulated joint angles at state-of-the-art accuracy and temporal stability with a very low number of cameras. In this paper, the kinematics of a joint with three degrees of freedom for a novel hyper-redundant robot arm is investigated. This joint is able to achieve a superposed rotation about two axes (roll and pitch) and a translational motion along one axis as a common prismatic joint. The forward and inverse kinematics of the so-called Multi-Joint will be determined in a closed-form solution. Next, the reachable and suitable workspace will be worked out to determine the solution space of the inverse kinematics. Finally, the differential kinematics to compute the cartesian velocity and statics will be determined.