Maarten J. Korsten

Measurement Errors and Uncertainty

No matter what precautions are taken, there will always be a difference between the result of a measurement and the true value of a quantity. This difference is called the measurement error. A measurement is useless without a quantitative indication of the magnitude of that error. Such an indication is called the uncertainty. Without knowing the uncertainty, the comparison of a measurement result with a reference value or with results of other measurements cannot be made. This chapter addresses the problem of how to define measurement errors, uncertainty, and related terms. The chapter also addresses the question of how to determine the uncertainty in practice. Under this, it summarizes the related statistical issues. Further, various sources of errors and the various types of errors is discussed. Methods to specify these errors are also highlighted. The chapter concludes with some techniques used to reduce the effects of errors.

A statistical model to describe invariants extracted from a 3-D quadric surface patch and its applications in region-based recognition

A statistical model, describing noise-disturbed invariants extracted from a surface patch of a range image, has been developed and applied to region based pose estimation and classification of 3D quadrics. The Mahalanobis distance, which yields the same results as a Baysian classifier, is used for the classification of the surface patches. The results, compared with the Euclidean distance, appear to be much more reliable.

Systematic and computer-assisted design of measurement systems

In this paper, a new approach is presented for the user guided automatised design of measurement systems. Two concepts are presented: an adapted concept for describing a measurement system and a new concept for the design of a measurement system. For the design concept, a heterarchical implementation is proposed. The applicability of our approach is illustrated with an example from practice.

Robust 3-dimensional object recognition using stereo vision and geometric hashing

We propose a technique that combines geometric hashing with stereo vision. The idea is to use the robustness of geometric hashing to spurious data to overcome the correspondence problem, while the stereo vision setup enables direct model matching using the 3-D object models. Furthermore, because the matching technique relies on the relative positions of local features, we should be able to perform robust recognition even with partially occluded objects. We tested this approach with simple geometric objects using a corner point detector. We successfully recognized objects even in scenes where the objects were partially occluded by other objects. For complicated scenes, however, the limited set of model features and required amount of computing time, sometimes became a problem.

A study on backpropagation networks for parameter estimation from grey-scale images

A large number of experiments have been done on the basic research of parameter estimation from images with neural networks. To obtain a better estimation accuracy of parameters and to decrease needed storage space and computation time, the architecture of networks, the effective learning rate and momentum, and the selection of training set are investigated. A comparison of network performance to that of the least squares estimator is made. The internal representations in trained networks, i.e. input-to-hidden weight maps or measuring models, which include statistical features of training images and have a clear physical and geometrical meaning, and the internal components of output parameters given by outputs of hidden neurons are presented.<<ETX>>

The estimation of geometry and motion of a surface from image sequences by means of linearization of a parametric

A method is given to estimate the geometry and motion of a moving body surface from image sequences. To this aim a parametric model of the surface is used, in order to reformulate the problem to one of parameter estimation. After linearization of the model standard linear estimation methods can be used to estimate the parameters. The main contribution of this paper is that a method is provided to perform the linearization without specifying the model. Therefore structure from motion estimation and nonrigid body motion estimation can be performed regardless of the model.

Considering shape from shading as an estimation problem

This paper presents a method combining shape and shading models in order to obtain estimations of 3D shape parameters directly from image grey values. The problem is considered as an application of optimal parameter estimation theory, according to Liebelt 8 This theory has been applied previously, where the emphasis was laid on time-delay 2, and motion estimation 3, 5, 9. It is applied here to provide an environment in which somewhat more complicated models can be designed with relative ease and to indicate how the behaviour of the parameters can be investigated. A shading model is added, offering explicit prediction of image grey values. We consider the problem for a single image and for an image pair, showing the shade of the object at two consecutive points of time. The last problem requiresalso a model for the motion of the body. The resulting non-linear estimation problem is linearized about a last parameter guess 8,so that a linear estimator can be applied to compute a new estimate. The various stages of the modelling process are separated by introducing several coordinate systems. Coordinate transformations will show the object from other points of view, and perform an orthographic projection of the 3D scene into the 2D image plane. The explicit grey value prediction yields a template, having a definite extent in the image. Because of the shading model this method requires no gradient images, as in the case of motion estimation 6 or stereo 5. The gradients can be computed analytically. To demonstrate the usefulness and the flexibility of our method, we consider a solid cylinder, irradiated with X-rays. The image is a shadow image originating from the absorption of radiation by the cylinder. In section 2 some background is given about the theory of parameter estimation from digital images. In section 3 the various models for the shape and motion of the body and the imaging process are given. In section 4 and 5 we investigate the properties of the estimator. In section 4 identifiability and uniqueness of the parameters are considered, yielding the parameters, that can be estimated uniquely from the image data. In section 5 some examples are given, elucidating the stabilty properties of the algorithm. To conclude we mention the possibility to replace the motion model with a model connecting images taken from two different positions. Thus this method is also suited to handle a stereo configuration.

Reconfigurable architecture for real-time 3-D parameter estimation from image sequences

In this paper a multiprocessor architecture is proposed which is capable of handling real-time parameter estimation algorithms for estimating 3D body parameters from 2D image sequences. The implicit parallelism of the algorithm is used to obtain a highly efficient architecture while retaining modularity and flexibility. CONTENTS

Design of Measurement Systems

This chapter reviews the essential steps in the design and decision process. The design process is decomposed into a number of basic steps, with feedback loops and iteration sequences. Most of these studies distinguish three major levels—task definition, concept generation, and evaluation. Any design should start with a description of the requirements the system should finally be able to meet. Important specifications of a measurement system concern information handling performance; technical performance; environmental conditions; and economically related aspects. The design of a measurement system is not a trivial task. Even for the measurement of a single parameter, a variety of measurement principles is available, and for each principle many sensor types, measurement configurations and different ways of signal processing and data handling are available. This leads to an almost infinite number of possible measurement systems for each measurand.

Measurement of Chemical Quantities

This chapter discusses the basics of electrochemical sensing and sensors. As is the case with physical sensors in the electrical domain, the retrieved information can be represented by a voltage, a current, or an impedance. For chemical sensors based on electrochemical measuring principles, this subdivision turns out to be a fundamental one because different means of mass transport are involved. Information represented by a voltage, a current or an impedance is retrieved by potentiometric sensors, by amperometric sensors or by electrolyte conductivity sensors, respectively. This chapter describes some fundamentals of potentiometry, amperometry, and electrolyte conductivity.