Tom Kavli

ASMO—Dan algorithm for adaptive spline modelling of observation data

Nonlinear system identification by modelling the underlying relationships in observation data is an important application area for artificial neural networks and other learning paradigms. Splines have been used for scattered data interpolation, but the applications have mainly been restricted to low dimensional input spaces. This paper describes ASMOD, a new learning paradigm for higher dimensional data (> > 3) based on B-spline interpolation. The models can be trained online, and a method for step-wise model refinement is applied during model training for gradually increasing the modelling capability until the desired or best possible accuracy is obtained. For every refinement step a number of possible refinement actions are evaluated, and the one that gives the highest improvement of the model accuracy is chosen. The model structure is hence adapted to the modelling problem, giving a model of small size and high accuracy. ASMOD has very efficient implementations on serial computers. The scheme has been ...

Modelling and Compensating Measurement Errors Caused by Scattering in Time-Of-Flight Cameras

Recently, Range Imaging (RIM) cameras have become available that capture high resolution range images at video rate. Such cameras measure the distance from the scene for each pixel independently based upon a measured time of flight (TOF). Some cameras, such as the SwissRanger(tm) SR-3000, measure the TOF based on the phase shift of reflected light from a modulated light source. Such cameras are shown to be susceptible to severe distortions in the measured range due to light scattering within the lens and camera. Earlier work induced using a simplified Gaussian point spread function and inverse filtering to compensate for such distortions. In this work a method is proposed for how to identify and use generally shaped empirical models for the point spread function to get a more accurate compensation. The otherwise difficult inverse problem is solved by using the forward model iteratively, according to well established procedures from image restoration. Each iteration is done as a sequential process, starting with the brightest parts of the image and then moving sequentially to the least bright parts, with each step subtracting the estimated effects from the measurements. This approach gives a faster and more reliable compensation convergence. An average reduction of the error by more than 60% is demonstrated on real images. The computation load corresponds to one or two convolutions of the measured complex image with a real filter of the same size as the image.

An Evaluation of Confidence Bound Estimation Methods for Neural Networks

When artificial neural networks (ANN) are used in prediction problems, it is usually desirable that some form of confidence bound is placed on the predicted value. Methods to estimate the confidence bound are available. However, these methods are valid under certain assumptions, which are rarely satisfied in practice. The behavior of the estimated confidence bound is not well understood when the assumptions are violated. We have designed some test functions to examine the behavior. The experimental results give us some guidelines on how the confidence estimation methods should be used in our application, which is to predict rock porosity values from seismic data for oil reservoir characterisation.

Automatic segmentation of overlapping fish using shape priors

We present results from a study where we segment fish in images captured within fish cages. The ultimate goal is to use this information to extract the weight distribution of the fish within the cages. Statistical shape knowledge is added to a Mumford-Shah functional defining the image energy. The fish shape is represented explicitly by a polygonal curve, and the energy minimization is done by gradient descent. The images represent many challenges with a highly cluttered background, inhomogeneous lighting and several overlapping objects. We obtain good segmentation results for silhouette-like images containing relatively few fish. In this case, the fish appear dark on a light background and the image energy is well behaved. In cases with more difficult lighting conditions the contours evolve slowly and often get trapped in local minima.

System for estimation of pin bone positions in pre-rigor salmon

Current systems for automatic processing of salmon are not able to remove all bones from freshly slaughtered salmon. This is because some of the bones are attached to the flesh by tendons, and the fillet is damaged or the bones broken if the bones are pulled out. This paper describes a camera based system for determining the tendon positions in the tissue, so that the tendon can be cut with a knife and the bones removed. The location of the tendons deep in the tissue is estimated based on the position of a texture pattern on the fillet surface. Algorithms for locating this line-looking pattern, in the presence of several other similar-looking lines and significant other texture are described. The algorithm uses a model of the patterns location to achieve precision and speed, followed by a RANSAC/MLESAC inspired line fitting procedure. Close to the neck the pattern is barely visible; this is handled through a greedy search algorithm. We achieve a precision better than 3 mm for 78% of the fish using maximum 2 seconds processing time.

On ASMOD — An Algorithm for Empirical Modelling using Spline Functions

Empirical modelling algorithms build mathematical models of systems based on observed data. This chapter describes the theoretical foundation and principles of the ASMOD algorithm, including some improvements on the original algorithm. The ASMOD algorithm uses B-splines for representing general nonlinear models of several variables. The internal structure of the model is, through an incremental refinement procedure, automatically adapted to the dependencies observed in the data. Only input variables which are found of relevance are included in the model, and the dependency of different variables are decoupled when possible. This makes the model more parsimonious and also more transparent to the user. Case studies are included which confirm the usefulness of the algorithm.

Theoretical properties of the ASMOD algorithm for empirical modelling

Empirical modelling algorithms build mathematical models of systems based on observed data. In this paper we present an analysis of the ASMOD algorithm. ASMOD uses B-splines to represent general nonlinear models of several variables. The internal structure of the model is, through an incremental refinement procedure, automatically adapted to the dependencies observed in the data. We derive, using risk minimization theory, uniform upper and lower bounds on the expected value of the criterion function used for model estimation. The bounds are given in terms of the empirical value of the criterion function computed on a finite number of data points. We also analyse the asymptotic convergence properties of the algorithm, and under natural conditions we show convergence to a model which minimizes the expected value of the estimation criterion.

Analysis of the ASMOD Algorithm for Empirical Modelling

Abstract Empirical modelling algorithms build mathematical models of systems based on observed data, The ASMOD algorithm uses B-splines for representing general nonlinear models of several variables. The internal structure of the model is, through an incremental refinement procedure, automatically adapted to the dependencies observed in the data. In this paper we present a convergence analysis of the ASMOD algorithm. Both the finite sample and the asymptotic properties are considered. The analysis of the finite sample properties is based on risk minimisation theory, and uniform bounds on the expected value of the squared prediction error are derived.

Reservoir characterization from 3D seismic data using artificial neural networks and stochastic modelling techniques

For an accurate prediction of the production profile of a hydrocarbon reservoir an optimum assessment of the geological reservoir model is required. The reservoir architecture and litho-stratigraphic properties of the model are most important boundary conditions in the economic evaluation of the reservoir. Integration of data from different sources, with widely varying resolutions and accuracies is a pre-requisite to achieve this goal.