Regularized pointwise map recovery from functional correspondence

The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point-to-point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly-isometric, and easily extends to recovering the point-to-point correspondence in part-to-whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases

Fine-grained nociceptive maps in primary somatosensory cortex

Topographic maps of the receptive surface are a fundamental feature of neural organization in many sensory systems. While touch is finely mapped in the cerebral cortex, it remains controversial how precise any cortical nociceptive map may be. Given that nociceptive innervation density is relatively low on distal skin regions such as the digits, one might conclude that the nociceptive system lacks fine representation of these regions. Indeed, only gross spatial organization of nociceptive maps has been reported so far. However, here we reveal the existence of fine-grained somatotopy for nociceptive inputs to the digits in human primary somatosensory cortex (SI). Using painful nociceptive-selective laser stimuli to the hand, and phase-encoded fMRI analysis methods, we observed somatotopic maps of the digits in contralateral SI. These nociceptive maps were highly aligned with maps of non-painful tactile stimuli, suggesting comparable cortical representations for, and possible interactions between, mechanoreceptive and nociceptive signals. Our findings may also be valuable for future studies tracking the timecourse and the spatial pattern of plastic changes in cortical organization involved in chronic pain

Image registration with sparse approximations in parametric dictionaries

We examine in this paper the problem of image registration from the new perspective where images are given by sparse approximations in parametric dictionaries of geometric functions. We propose a registration algorithm that looks for an estimate of the global transformation between sparse images by examining the set of relative geometrical transformations between the respective features. We propose a theoretical analysis of our registration algorithm and we derive performance guarantees based on two novel important properties of redundant dictionaries, namely the robust linear independence and the transformation inconsistency. We propose several illustrations and insights about the importance of these dictionary properties and show that common properties such as coherence or restricted isometry property fail to provide sufficient information in registration problems. We finally show with illustrative experiments on simple visual objects and handwritten digits images that our algorithm outperforms baseline competitor methods in terms of transformation-invariant distance computation and classification