We present a simple and fast mesh denoising method, which can remove noise effectively, while preserving mesh features such as sharp edges and corners. The method consists of two stages. Firstly, noisy face normals are filtered iteratively by weighted averaging of neighboring face normals. Secondly, vertex positions are iteratively updated to agree with the denoised face normals. The weight function used during normal filtering is much simpler than that used in previous similar approaches, being simply a trimmed quadratic. This makes the algorithm both fast and simple to implement. Vertex position updating is based on the integration of surface normals using a least-squares error criterion. Like previous algorithms, we solve the least-squares problem by gradient descent, but whereas previous methods needed user input to determine the iteration step size, we determine it automatically. In addition, we prove the convergence of the vertex position updating approach. Analysis and experiments show the advantages of our proposed method over various earlier surface denoising methods.

Abstract-3D surface registration transforms multiple 3D datasets into the same coordinate system so as to align overlapping components of these sets. Recent surveys have covered different aspects of either rigid or non-rigid registration, but seldom discuss them as a whole. Our study serves two purposes: (i) to give a comprehensive survey of both types of registration, focusing on 3D point clouds and meshes, and (ii) to provide a better understanding of registration from the perspective of data fitting. Registration is closely related to data fitting in that it comprises three core interwoven components: model selection, correspondences & constraints and optimization. Study of these components (i) provides a basis for comparison of the novelties of different techniques, (ii) reveals the similarity of rigid and non-rigid registration in terms of problem representations, and (iii) shows how over-fitting arises in non-rigid registration and the reasons for increasing interest in intrinsic techniques. We further summarise some practical issues of registration which include initializations and evaluations, and discuss some of our own observations, insights and foreseeable research trends.

Bas-reliefs are a form of flattened artwork, part-way between 3D sculpture and 2D painting. Recent research has considered automatic bas-relief generation from 3D scenes. However, little work has addressed the generation of bas-reliefs from 2D images. In this paper, we propose a method to automatically generate bas-relief surfaces from frontal photographs of human faces, with potential applications to e.g. coinage and commemorative medals.Our method has two steps. Starting from a photograph of a human face, we first generate a plausible image of a bas-relief of the same face. Secondly, we apply shape-from-shading to this generated bas-relief image to determine the 3D shape of the final bas-relief. To model the mapping from an input photograph to the image of a corresponding bas-relief, we use a feedforward network. The training data comprises images generated from an input 3D model of a face, and images generated from a corresponding bas-relief; the latter is produced by an existing 3D model-to-bas-relief algorithm. A saliency map of the face controls both model building, and bas-relief generation.Our experimental results demonstrate that the generated bas-relief surfaces are smooth and plausible, with correct global geometric nature, the latter giving them a stable appearance under changes of viewing direction and illumination.

Information encoded in networks of stationary, interacting spin-1/2 particles is central for many applications ranging from quantum spintronics to quantum information processing. Without control, however, information transfer through such networks is generally inefficient. Currently available control methods to maximize the transfer fidelities and speeds mainly rely on dynamic control using time-varying fields and often assume instantaneous readout. We present an alternative approach to achieving efficient, high-fidelity transfer of excitations by shaping the energy landscape via the design of time-invariant feedback control laws without recourse to dynamic control. Both instantaneous readout and the more realistic case of finite readout windows are considered. The technique can also be used to freeze information by designing energy landscapes that achieve Anderson localization. Perfect state or super-optimal transfer and localization are enabled by conditions on the eigenstructure of the system and signature properties for the eigenvectors. Given the eigenstructure enabled by super-optimality, it is shown that feedback controllers that achieve perfect state transfer are, surprisingly, also the most robust with regard to uncertainties in the system and control parameters.

Finding design intent embodied as high-level geometric relations between a CAD model's sub-parts facilitates various tasks such as model editing and analysis. This is especially important for boundary-representation models arising from, e.g., reverse engineering or CAD data transfer. These lack explicit information about design intent, and often the intended geometric relations are only approximately present. The novel solution to this problem presented is based on detecting approximate local incomplete symmetries, in a hierarchical decomposition of the model into simpler, more symmetric sub-parts. Design intent is detected as congruencies, symmetries and symmetric arrangements of the leaf-parts in this decomposition. All elementary 3D symmetry types and common symmetric arrangements are considered. They may be present only locally in subsets of the leaf-parts, and may also be incomplete, i.e. not all elements required for a symmetry need be present. Adaptive tolerance intervals are detected automatically for matching interpoint distances, enabling efficient, robust and consistent detection of approximate symmetries. Doing so avoids finding many spurious relations, reliably resolves ambiguities between relations, and reduces inconsistencies. Experiments show that detected relations reveal significant design intent.