Implicit Surface Modelling with a Globally Regularised Basis of Compact Support

We consider the problem of constructing a globally smooth analytic function that represents a surface implicitly by way of its zero set, given sample points with surface normal vectors. The contributions of the paper include a novel means of regularising multi-scale compactly supported basis functions that leads to the desirable interpolation properties previously only associated with fully supported bases. We also provide a regularisation framework for simpler and more direct treatment of surface normals, along with a corresponding generalisation of the representer theorem lying at the core of kernel-based machine learning methods. We demonstrate the techniques on 3D problems of up to 14 million data points, as well as 4D time series data and four-dimensional interpolation between three-dimensional shapes

Implicit surfaces with globally regularised and compactly supported basis functions

We consider the problem of constructing a function whose zero set is to represent a surface, given sample points with surface normal vectors. The contributions include a novel means of regularising multi-scale compactly supported basis functions that leads to the desirable properties previously only associated with fully supported bases, and show equivalence to a Gaussian process with modified covariance function. We also provide a regularisation framework for simpler and more direct treatment of surface normals, along with a corresponding generalisation of the representer theorem. We demonstrate the techniques on 3D problems of up to 14 million data points, as well as 4D time series data

Brain tumor visualization for magnetic resonance images using modified shape-based interpolation method

3D visualization plays an essential role in medical diagnosis and setting treatment plans especially for brain cancer. There have been many attempts for brain tumor reconstruction and visualization using various techniques. However, this problem is still considered unsolved as more accurate results are needed in this critical field. In this paper, a sequence of 2D slices of brain magnetic resonance Images was used to reconstruct a 3D model for the brain tumor. The images were automatically segmented using a wavelet multi-resolution expectation maximization algorithm. Then, the inter-slice gaps were interpolated using the proposed modified shape-based interpolation method. The method involves three main steps; transferring the binary tumor images to distance images using a suitable distance function, interpolating the distance images using cubic spline interpolation and thresholding the interpolated values to get the reconstructed slices. The final tumor is then visualized as a 3D isosurface. We evaluated the proposed method by removing an original slice from the input images and interpolating it, the results outperform the original shape-based interpolation method by an average of 3% reaching 99% of accuracy for some slice images

Parameterization of point-cloud freeform surfaces using adaptive sequential learning RBFnetworks

We propose a self-organizing Radial Basis Function (RBF) neural network method for parameterization of freeform surfaces from larger, noisy and unoriented point clouds. In particular, an adaptive sequential learning algorithm is presented for network construction from a single instance of point set. The adaptive learning allows neurons to be dynamically inserted and fully adjusted (e.g. their locations, widths and weights), according to mapping residuals and data point novelty associated to underlying geometry. Pseudo-neurons, exhibiting very limited contributions, can be removed through a pruning procedure. Additionally, a neighborhood extended Kalman filter (NEKF) was developed to significantly accelerate parameterization. Experimental results show that this adaptive learning enables effective capture of global low-frequency variations while preserving sharp local details, ultimately leading to accurate and compact parameterization, as characterized by a small number of neurons. Parameterization using the proposed RBF network provides simple, low cost and low storage solutions to many problems such as surface construction, re-sampling, hole filling, multiple level-of-detail meshing and data compression from unstructured and incomplete range data. Performance results are also presented for comparison

A Knowledge Integration Framework for 3D Shape Reconstruction

The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points in sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment in which the robots operate with. This means unstructured 3D samples must be processed by application-specific models to enable a robot, for instance, to detect and identify objects and infer the scene geometry for path-planning more efficiently than by using raw 3D data. This thesis specifically focuses on the fundamental task of 3D shape reconstruction and modelling by presenting a new knowledge integration framework for unstructured 3D samples. The novelty lies in the representation of surfaces by algebraic functions with limited support, which enables the extraction of smooth consistent shapes from noisy samples with a heterogeneous density. Moreover, many surfaces in urban environments can reasonably be assumed to be planar, and the framework exploits this knowledge to enable effective noise suppression without loss of detail. This is achieved by using a convex optimization technique which has linear computational complexity. Thus is much more efficient than existing solutions. The new framework has been validated by critical experimental analysis and evaluation and has been shown to increase the accuracy of the reconstructed shape significantly compared to state-of-the-art methods. Applying this new knowledge integration framework means that less accurate, low-cost 3D sensors can be employed without sacrificing the high demands that 3D perception must achieve. This links well into the area of robotic inspection, as for example regarding small drones that use inaccurate and lightweight image sensors