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Laurent Gajny

Publications and source records attributed to Laurent Gajny.

3 recordsLinked to original sources

Field Converter: Geometry-Initialized Temporal Residual Refinement for World-Grounded Player Pose Estimation from Soccer Broadcasts

Recovering 3D human pose from monocular sports broadcasts remains challenging when players must be localized in a shared metric world coordinate system rather than only reconstructed relative to their own body. We introduce Field Converter, a geometry-initialized temporal residual framework for world-grounded 3D player pose estimation from calibrated soccer broadcasts. Our method first uses camera and pitch geometry to initialize the player root through ray-ground intersection, then predicts a temporal residual correction from pose, image, camera, and geometric cues. On match-disjoint evaluation sequences, residual refinement reduces root error from 49cm with geometry alone to 14cm with a frame-wise MLP and 10cm with a TCN, while a Transformer achieves a comparable 11cm. The resulting world-space MPJPE reaches 13.2cm, and ablations show that residual prediction clearly outperforms direct global-root regression while temporal context matters more than the specific temporal backbone. Failure analysis further identifies airborne motion as the main limitation of the ground-based geometric initialization.

cs.CV↗

Best $L_1$ approximation of Heaviside-type functions in Chebyshev and weak-Chebyshev spaces

In this article, we study the problem of best $L_1$ approximation of Heaviside-type functions in Chebyshev and weak-Chebyshev spaces. We extend the Hobby-Rice theorem into an appropriate framework and prove the unicity of best $L_1$ approximation of Heaviside-type functions in an even-dimensional Chebyshev space under the condition that the dimension of the subspace composed of the even functions is half the dimension of the whole space. We also apply the results to compute best $L_1$ approximations of Heaviside-type functions by polynomials and Hermite polynomial splines with fixed knots.

math.FA↗

$L_1$ spline fits via sliding window process : continuous and discrete cases

Best $L_1$ approximation of the Heaviside function and best $\ell_1$ approximation of multiscale univariate datasets by cubic splines have a Gibbs phenomenon. Numerical experiments show that it can be reduced by using $L_1$ spline fits which are best $L_1$ approximations in an appropriate spline space obtained by the union of $L_1$ interpolation splines. We prove here the existence of $L_1$ spline fits which has never been done to the best of our knowledge. Their major disadvantage is that obtaining them can be time consuming. Thus we propose a sliding window method on seven nodes which is as efficient as the global method both for functions and datasets with abrupt changes of magnitude but within a linear complexity on the number of spline nodes.

math.NA↗