Hybrid Functional-Neural Approach for Surface Reconstruction

ABSTRACT. This paper introduces a new hybrid functional-neural approach for surface reconstruction. Our approach is based on the combination of two powerful artificial intelligence paradigms: on one hand, we apply the popular Kohonen neural network to address the data parameterization problem. On the other hand, we introduce a new functional network, called NURBS functional network, whose topology is aimed at reproducing faithfully the functional structure of the NURBS surfaces. These neural and functional networks are applied in an iterative fashion for further surface refinement. The hybridization of these two networks provides us with a powerful computational approach to obtain a NURBS fitting surface to a set of irregularly sampled noisy data points within a prescribed error threshold. The method has been applied to two illustrative examples. The experimental results confirm the good performance of our approach.This research has been kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project ref. no. TIN2012-30768, Toho University (Funabashi, Japan), and the University of Cantabria (Santander, Spain)

Differentiable Uncalibrated Imaging

We propose a differentiable imaging framework to address uncertainty in measurement coordinates such as sensor locations and projection angles. We formulate the problem as measurement interpolation at unknown nodes supervised through the forward operator. To solve it we apply implicit neural networks, also known as neural fields, which are naturally differentiable with respect to the input coordinates. We also develop differentiable spline interpolators which perform as well as neural networks, require less time to optimize and have well-understood properties. Differentiability is key as it allows us to jointly fit a measurement representation, optimize over the uncertain measurement coordinates, and perform image reconstruction which in turn ensures consistent calibration. We apply our approach to 2D and 3D computed tomography and show that it produces improved reconstructions compared to baselines that do not account for the lack of calibration. The flexibility of the proposed framework makes it easy to apply to almost arbitrary imaging problems

Deep learning cardiac motion analysis for human survival prediction

Motion analysis is used in computer vision to understand the behaviour of moving objects in sequences of images. Optimising the interpretation of dynamic biological systems requires accurate and precise motion tracking as well as efficient representations of high-dimensional motion trajectories so that these can be used for prediction tasks. Here we use image sequences of the heart, acquired using cardiac magnetic resonance imaging, to create time-resolved three-dimensional segmentations using a fully convolutional network trained on anatomical shape priors. This dense motion model formed the input to a supervised denoising autoencoder (4Dsurvival), which is a hybrid network consisting of an autoencoder that learns a task-specific latent code representation trained on observed outcome data, yielding a latent representation optimised for survival prediction. To handle right-censored survival outcomes, our network used a Cox partial likelihood loss function. In a study of 302 patients the predictive accuracy (quantified by Harrell's C-index) was significantly higher (p < .0001) for our model C=0.73 (95$\%$ CI: 0.68 - 0.78) than the human benchmark of C=0.59 (95$\%$ CI: 0.53 - 0.65). This work demonstrates how a complex computer vision task using high-dimensional medical image data can efficiently predict human survival

Immunological-based approach for accurate fitting of 3D noisy data points with Bézier surfaces

Free-form parametric surfaces are common tools nowadays in many applied fields, such as Computer-Aided Design & Manufacturing (CAD/CAM), virtual reality, medical imaging, and many others. A typical problem in this setting is to fit surfaces to 3D noisy data points obtained through either laser scanning or other digitizing methods, so that the real data from a physical object are transformed back into a fully usable digital model. In this context, the present paper describes an immunologicalbased approach to perform this process accurately by using the classical free-form Bézier surfaces. Our method applies a powerful bio-inspired paradigm called Artificial Immune Systems (AIS), which is receiving increasing attention from the scientific community during the last few years because of its appealing computational features. The AIS can be understood as a computational methodology based upon metaphors of the biological immune system of humans and other mammals. As such, there is not one but several AIS algorithms. In this chapter we focus on the clonal selection algorithm (CSA), which explicitly takes into account the affinity maturation of the immune response. The paper describes how the CSA algorithm can be effectively applied to the accurate fitting of 3D noisy data points with Bézier surfaces. To this aim, the problem to be solved as well as the main steps of our solving method are described in detail. Some simple yet illustrative examples show the good performance of our approach. Our method is conceptually simple to understand, easy to implement, and very general, since no assumption is made on the set of data points or on the underlying function beyond its continuity. As a consequence, it can be successfully applied even under challenging situations, such as the absence of any kind of information regarding the underlying function of data

Tabu search-based method for bézier curve parameterization

A very important issue in many applied fields is to construct the fitting curve that approximates a given set of data points optimally in the sense of least-squares. This problem arises in a number of areas, such as computer-aided design & manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. This is also a hard problem, because it is highly nonlinear, over-determined and typically involves a large number of unknown variables. A critical step in this process is to obtain a suitable parameterization of the data points. In this context, this paper introduces a new method to obtain an optimal solution for the parameterization problem of the least-squares fitting Bézier curve. Our method is based on a local search metaheuristic approach for optimization problems called tabu search. The method is applied to some simple yet illustrative examples for the cases of 2D and 3D curves. The proposed method is simple to understand, easy to implement and can be applied to any kind of smooth data points. Our experimental results show that the presented method performs very well, being able to fit the data points with a high degree of accuracy.This research has been financially supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project Ref. #TIN2012-30768, Toho University, the University of Cantabria, and the Instituto de Física de Cantabria, a mixed research center of the University of Cantabria and CSIC-Consejo Superior de Investigaciones Científicas.Peer Reviewe

Memetic electromagnetism algorithm for surface reconstruction with rational bivariate Bernstein basis functions

Surface reconstruction is a very important issue with outstanding applications in fields such as medical imaging (computer tomography, magnetic resonance), biomedical engineering (customized prosthesis and medical implants), computer-aided design and manufacturing (reverse engineering for the automotive, aerospace and shipbuilding industries), rapid prototyping (scale models of physical parts from CAD data), computer animation and film industry (motion capture, character modeling), archaeology (digital representation and storage of archaeological sites and assets), virtual/augmented reality, and many others. In this paper we address the surface reconstruction problem by using rational Bézier surfaces. This problem is by far more complex than the case for curves we solved in a previous paper. In addition, we deal with data points subjected to measurement noise and irregular sampling, replicating the usual conditions of real-world applications. Our method is based on a memetic approach combining a powerful metaheuristic method for global optimization (the electromagnetism algorithm) with a local search method. This method is applied to a benchmark of five illustrative examples exhibiting challenging features. Our experimental results show that the method performs very well, and it can recover the underlying shape of surfaces with very good accuracy.This research is kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project #TIN2012-30768, Toho University, and the University of Cantabria. The authors are particularly grateful to the Department of Information Science of Toho University for all the facilities given to carry out this work. We also thank the Editor and the two anonymous reviewers who helped us to improve our paper with several constructive comments and suggestions