Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies

In motion analysis and understanding it is important to be able to fit a suitable model or structure to the temporal series of observed data, in order to describe motion patterns in a compact way, and to discriminate between them. In an unsupervised context, i.e., no prior model of the moving object(s) is available, such a structure has to be learned from the data in a bottom-up fashion. In recent times, volumetric approaches in which the motion is captured from a number of cameras and a voxel-set representation of the body is built from the camera views, have gained ground due to attractive features such as inherent view-invariance and robustness to occlusions. Automatic, unsupervised segmentation of moving bodies along entire sequences, in a temporally-coherent and robust way, has the potential to provide a means of constructing a bottom-up model of the moving body, and track motion cues that may be later exploited for motion classification. Spectral methods such as locally linear embedding (LLE) can be useful in this context, as they preserve "protrusions", i.e., high-curvature regions of the 3D volume, of articulated shapes, while improving their separation in a lower dimensional space, making them in this way easier to cluster. In this paper we therefore propose a spectral approach to unsupervised and temporally-coherent body-protrusion segmentation along time sequences. Volumetric shapes are clustered in an embedding space, clusters are propagated in time to ensure coherence, and merged or split to accommodate changes in the body's topology. Experiments on both synthetic and real sequences of dense voxel-set data are shown. This supports the ability of the proposed method to cluster body-parts consistently over time in a totally unsupervised fashion, its robustness to sampling density and shape quality, and its potential for bottom-up model constructionComment: 31 pages, 26 figure

Coarse-to-Fine Annotation Enrichment for Semantic Segmentation Learning

Rich high-quality annotated data is critical for semantic segmentation learning, yet acquiring dense and pixel-wise ground-truth is both labor- and time-consuming. Coarse annotations (e.g., scribbles, coarse polygons) offer an economical alternative, with which training phase could hardly generate satisfactory performance unfortunately. In order to generate high-quality annotated data with a low time cost for accurate segmentation, in this paper, we propose a novel annotation enrichment strategy, which expands existing coarse annotations of training data to a finer scale. Extensive experiments on the Cityscapes and PASCAL VOC 2012 benchmarks have shown that the neural networks trained with the enriched annotations from our framework yield a significant improvement over that trained with the original coarse labels. It is highly competitive to the performance obtained by using human annotated dense annotations. The proposed method also outperforms among other state-of-the-art weakly-supervised segmentation methods.Comment: CIKM 2018 International Conference on Information and Knowledge Managemen

Differentiability of fractal curves

While self-similar sets have no tangents at any single point, self-affine curves can be smooth. We consider plane self-affine curves without double points and with two pieces. There is an open subset of parameter space for which the curve is differentiable at all points except for a countable set. For a parameter set of codimension one, the curve is continuously differentiable. However, there are no twice differentiable self-affine curves in the plane, except for parabolic arcs