  Statistical body shape models are widely used in 3D pose estimation due to
their low-dimensional parameters representation. However, it is difficult to
avoid self-intersection between body parts accurately. Motivated by this fact,
we proposed a novel self-intersection penalty term for statistical body shape
models applied in 3D pose estimation. To avoid the trouble of computing
self-intersection for complex surfaces like the body meshes, the gradient of
our proposed self-intersection penalty term is manually derived from the
perspective of geometry. First, the self-intersection penalty term is defined
as the volume of the self-intersection region. To calculate the partial
derivatives with respect to the coordinates of the vertices, we employed
detection rays to divide vertices of statistical body shape models into
different groups depending on whether the vertex is in the region of
self-intersection. Second, the partial derivatives could be easily derived by
the normal vectors of neighboring triangles of the vertices. Finally, this
penalty term could be applied in gradient-based optimization algorithms to
remove the self-intersection of triangular meshes without using any
approximation. Qualitative and quantitative evaluations were conducted to
demonstrate the effectiveness and generality of our proposed method compared
with previous approaches. The experimental results show that our proposed
penalty term can avoid self-intersection to exclude unreasonable predictions
and improves the accuracy of 3D pose estimation indirectly. Further more, the
proposed method could be employed universally in triangular mesh based 3D
reconstruction.
