Dan Raviv

Active Printed Materials for Complex Self-Evolving Deformations

We propose a new design of complex self-evolving structures that vary over time due to environmental interaction. In conventional 3D printing systems, materials are meant to be stable rather than active and fabricated models are designed and printed as static objects. Here, we introduce a novel approach for simulating and fabricating self-evolving structures that transform into a predetermined shape, changing property and function after fabrication. The new locally coordinated bending primitives combine into a single system, allowing for a global deformation which can stretch, fold and bend given environmental stimulus.

Full and Partial Symmetries of Non-rigid Shapes

Symmetry and self-similarity are the cornerstone of Nature, exhibiting themselves through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection of asymmetries is important in numerous practical applications, including crystallography, medical imaging, and face recognition, to mention a few. Conversely, the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis. Traditionally, symmetries are described as extrinsic geometric properties of the shape. While being adequate for rigid shapes, such a description is inappropriate for non-rigid ones: extrinsic symmetry can be broken as a result of shape deformations, while its intrinsic symmetry is preserved. In this paper, we present a generalization of symmetries for non-rigid shapes and a numerical framework for their analysis, addressing the problems of full and partial exact and approximate symmetry detection and classification.

Symmetries of non-rigid shapes

Symmetry and self-similarity is the cornerstone of Nature, exhibiting itself through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection of asymmetries is important in numerous practical applications, including crystallography, medical imaging, and face recognition, to mention a few. Conversely, the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis. Traditionally, symmetries are described as extrinsic geometric properties of the shape. While being adequate for rigid shapes, such a description is inappropriate for non-rigid ones. Extrinsic symmetry can be broken as a result of shape deformations, while its intrinsic symmetry is preserved. In this paper, we pose the problem of finding intrinsic symmetries of non-rigid shapes and propose an efficient method for their computation.

Volumetric heat kernel signatures

Invariant shape descriptors are instrumental in numerous shape analysis tasks including deformable shape comparison, registration, classification, and retrieval. Most existing constructions model a 3D shape as a two-dimensional surface describing the shape boundary, typically represented as a triangular mesh or a point cloud. Using intrinsic properties of the surface, invariant descriptors can be designed. One such example is the recently introduced heat kernel signature, based on the Laplace-Beltrami operator of the surface. In many applications, however, a volumetric shape model is more natural and convenient. Moreover, modeling shape deformations as approximate isometries of the volume of an object, rather than its boundary, better captures natural behavior of non-rigid deformations in many cases. Here, we extend the idea of heat kernel signature to robust isometry-invariant volumetric descriptors, and show their utility in shape retrieval. The proposed approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark.

Locating and classifying fluorescent tags behind turbid layers using time-resolved inversion

The use of fluorescent probes and the recovery of their lifetimes allow for significant advances in many imaging systems, in particular, medical imaging systems. Here we propose and experimentally demonstrate reconstructing the locations and lifetimes of fluorescent markers hidden behind a turbid layer. This opens the door to various applications for non-invasive diagnosis, analysis, flowmetry and inspection. The method is based on a time-resolved measurement that captures information about both fluorescence lifetime and spatial position of the probes. To reconstruct the scene, the method relies on a sparse optimization framework to invert time-resolved measurements. This wide-angle technique does not rely on coherence, and does not require the probes to be directly in line of sight of the camera, making it potentially suitable for long-range imaging.

Affine-invariant diffusion geometry for the analysis of deformable 3D shapes

We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant Laplacian from which local and global geometric structures are extracted. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis.

Scale Invariant Geometry for Nonrigid Shapes

In nature, different animals of the same species frequently exhibit local variations in scale. New developments in shape matching research thus increasingly provide us with the tools to answer such fascinating questions as the following: How should we measure the discrepancy between a small dog with large ears and a large one with small ears? Are there geometric structures common to both an elephant and a giraffe? What is the morphometric similarity between a blue whale and a dolphin? Currently, there are only two methods that allow us to quantify similarities between surfaces which are insensitive to deformations in size: scale invariant local descriptors and global normalization methods. Here, we propose a new tool for shape exploration. We introduce a scale invariant metric for surfaces that allows us to analyze nonrigid shapes, generate locally invariant features, produce scale invariant geodesics, embed one surface into another despite changes in local and global size, and assist in the computational...

Short Communication to SMI 2011: Affine-invariant geodesic geometry of deformable 3D shapes

Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in R^3 in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine-invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis.

Affine-invariant photometric heat kernel signatures

In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local shape descriptors. Our construction is based on the definition of a modified metric, which combines geometric and photometric information, and then the diffusion process on the shape manifold is simulated. Experimental results show that such data fusion is useful in coping with shape retrieval experiments, where pure geometric and pure photometric methods fail. Apart from retrieval task the proposed diffusion process may be employed in other applications.

Pose estimation using time-resolved inversion of diffuse light

We present a novel approach for evaluation of position and orientation of geometric shapes from scattered time-resolved data. Traditionally, imaging systems treat scattering as unwanted and are designed to mitigate the effects. Instead, we show here that scattering can be exploited by implementing a system based on a femtosecond laser and a streak camera. The result is accurate estimation of object pose, which is a fundamental tool in analysis of complex scenarios and plays an important role in our understanding of physical phenomena. Here, we experimentally show that for a given geometry, a single incident illumination point yields enough information for pose estimation and tracking after multiple scattering events. Our technique can be used for single-shot imaging behind walls or through turbid media.