Consistent ICP for the registration of sparse and inhomogeneous point clouds

In this paper, we derive a novel iterative closest point (ICP) technique that performs point cloud alignment in a robust and consistent way. Traditional ICP techniques minimize the point-to-point distances, which are successful when point clouds contain no noise or clutter and moreover are dense and more or less uniformly sampled. In the other case, it is better to employ point-to-plane or other metrics to locally approximate the surface of the objects. However, the point-to-plane metric does not yield a symmetric solution, i.e. the estimated transformation of point cloud p to point cloud q is not necessarily equal to the inverse transformation of point cloud q to point cloud p. In order to improve ICP, we will enforce such symmetry constraints as prior knowledge and make it also robust to noise and clutter. Experimental results show that our method is indeed much more consistent and accurate in presence of noise and clutter compared to existing ICP algorithms

M\"obius Invariants of Shapes and Images

Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to this problem is to identify the group of possible transformations of the object and to find invariants to the action of that group, meaning that the object has the same values of the invariants despite the action of the group. In this paper we study the invariants of planar shapes and images under the M\"obius group $\mathrm{PSL}(2,\mathbb{C})$, which arises in the conformal camera model of vision and may also correspond to neurological aspects of vision, such as grouping of lines and circles. We survey properties of invariants that are important in applications, and the known M\"obius invariants, and then develop an algorithm by which shapes can be recognised that is M\"obius- and reparametrization-invariant, numerically stable, and robust to noise. We demonstrate the efficacy of this new invariant approach on sets of curves, and then develop a M\"obius-invariant signature of grey-scale images

Component-wise modeling of articulated objects

We introduce a novel framework for modeling articulated objects based on the aspects of their components. By decomposing the object into components, we divide the problem in smaller modeling tasks. After obtaining 3D models for each component aspect by employing a shape deformation paradigm, we merge them together, forming the object components. The final model is obtained by assembling the components using an optimization scheme which fits the respective 3D models to the corresponding apparent contours in a reference pose. The results suggest that our approach can produce realistic 3D models of articulated objects in reasonable time

Exploiting lattice structures in shape grammar implementations

The ability to work with ambiguity and compute new designs based on both defined and emergent shapes are unique advantages of shape grammars. Realizing these benefits in design practice requires the implementation of general purpose shape grammar interpreters that support: (a) the detection of arbitrary subshapes in arbitrary shapes and (b) the application of shape rules that use these subshapes to create new shapes. The complexity of currently available interpreters results from their combination of shape computation (for subshape detection and the application of rules) with computational geometry (for the geometric operations need to generate new shapes). This paper proposes a shape grammar implementation method for three-dimensional circular arcs represented as rational quadratic Bézier curves based on lattice theory that reduces this complexity by separating steps in a shape computation process from the geometrical operations associated with specific grammars and shapes. The method is demonstrated through application to two well-known shape grammars: Stiny's triangles grammar and Jowers and Earl's trefoil grammar. A prototype computer implementation of an interpreter kernel has been built and its application to both grammars is presented. The use of Bézier curves in three dimensions opens the possibility to extend shape grammar implementations to cover the wider range of applications that are needed before practical implementations for use in real life product design and development processes become feasible

Towards segmentation and spatial alignment of the human embryonic brain using deep learning for atlas-based registration

We propose an unsupervised deep learning method for atlas based registration to achieve segmentation and spatial alignment of the embryonic brain in a single framework. Our approach consists of two sequential networks with a specifically designed loss function to address the challenges in 3D first trimester ultrasound. The first part learns the affine transformation and the second part learns the voxelwise nonrigid deformation between the target image and the atlas. We trained this network end-to-end and validated it against a ground truth on synthetic datasets designed to resemble the challenges present in 3D first trimester ultrasound. The method was tested on a dataset of human embryonic ultrasound volumes acquired at 9 weeks gestational age, which showed alignment of the brain in some cases and gave insight in open challenges for the proposed method. We conclude that our method is a promising approach towards fully automated spatial alignment and segmentation of embryonic brains in 3D ultrasound