A kinematic-geometric model based on ankles' depth trajectory in frontal plane for gait analysis using a single RGB-D camera.

The emergence of RGB-D cameras and the development of pose estimation algorithms offer opportunities in biomechanics. However, some challenges still remain when using them for gait analysis, including noise which leads to misidentification of gait events and inaccuracy. Therefore, we present a novel kinematic-geometric model for spatio-temporal gait analysis, based on ankles' trajectory in the frontal plane and distance-to-camera data (depth). Our approach consists of three main steps: identification of the gait pattern and modeling via parameterized curves, development of a fitting algorithm, and computation of locomotive indices. The proposed fitting algorithm applies on both ankles' depth data simultaneously, by minimizing through numerical optimization some geometric and biomechanical error functions. For validation, 15 subjects were asked to walk inside the walkway of the OptoGait, while the OptoGait and an RGB-D camera (Microsoft Azure Kinect) were both recording. Then, the spatio-temporal parameters of both feet were computed using the OptoGait and the proposed model. Validation results show that the proposed model yields good to excellent absolute statistical agreement (0.86 ≤ Rc ≤ 0.99). Our kinematic-geometric model offers several benefits: (1) It relies only on the ankles' depth trajectory both for gait events extraction and spatio-temporal parameters' calculation; (2) it is usable with any kind of RGB-D camera or even with 3D marker-based motion analysis systems in absence of toes' and heels' markers; and (3) it enables improving the results by denoising and smoothing the ankles' depth trajectory. Hence, the proposed kinematic-geometric model facilitates the development of portable markerless systems for accurate gait analysis.

Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement.

Surface remeshing is a key component in many geometry processing applications. The typical goal consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application (e.g., the minimum interior angle is above an application-dependent threshold). Our algorithm is designed to address all three optimization goals simultaneously by targeting prescribed bounds on approximation error , minimal interior angle and maximum mesh complexity (number of vertices). The approximation error bound is a hard constraint, while the other two criteria are modeled as optimization goals to guarantee feasibility. Our optimization framework applies carefully prioritized local operators in order to greedily search for the coarsest mesh with minimal interior angle above and approximation error bounded by . Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that for reasonable angle bounds ( ) our approach delivers high-quality meshes with implicitly preserved features (no tagging required) and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.