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2009 | Buch

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Image Correlation for Shape, Motion and Deformation Measurements

Basic Concepts,Theory and Applications

verfasst von: Hubert Schreier, Jean-José Orteu, Michael A. Sutton

Verlag: Springer US

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Image Correlation for Shape, Motion and Deformation Measurements provides a comprehensive overview of data extraction through image analysis. Readers will find and in-depth look into various single- and multi-camera models (2D-DIC and 3D-DIC), two- and three-dimensional computer vision, and volumetric digital image correlation (VDIC). Fundamentals of accurate image matching are described, along with presentations of both new methods for quantitative error estimates in correlation-based motion measurements, and the effect of out-of-plane motion on 2D measurements. Thorough appendices offer descriptions of continuum mechanics formulations, methods for local surface strain estimation and non-linear optimization, as well as terminology in statistics and probability.

With equal treatment of computer vision fundamentals and techniques for practical applications, this volume is both a reference for academic and industry-based researchers and engineers, as well as a valuable companion text for appropriate vision-based educational offerings.

Inhaltsverzeichnis

Frontmatter

1. Introduction

As used in this article, the term "digital image correlation" refers to the class of non-contacting methods that acquire images of an object, store images in digital form and perform image analysis to extract full-field shape, deformation and/or motion measurements. Digital image registration (i.e. matching) has been performed with many types of object-based patterns, including lines, grids, dots and random arrays. One of the most commonly used approaches employs random patterns and compares sub-regions throughout the image to obtain a full-field of measurements. The patterns may occur on solid surfaces or may be a collection of particles in a fluid medium.

Michael A. Michael A., Jean-José Orteu, Hubert W. Schreier

2. Elements of Geometrical Optics

Figure 2.1 shows a simple optical system that consists of a single, ideal lens, i.e. a thin lens. Such lenses are good approximations when (a) the angles and diameters of the focused, light rays are sufficiently small so that the Gauss approximation is appropriate and (b) geometrical aberrations and other optical defects can be neglected [107]. Next, we consider an optical system consisting of a single thick lens. Using ray optics to extract the basic formulae relating object positions to sensor locations, we will see that by neglecting the effect of blur due to defocus, these optical models can be combined into a single simple geometric model of perspective projection: the so-called pinhole model.

Michael A. Michael A., Jean-José Orteu, Hubert W. Schreier

3. Single Camera Models and Calibration Procedures in Computer Vision

A camera is typically an opto-electronic device consisting of several sub-systems. First is the optics, consisting of elements such as a series of lenses, optical filters and shuttering elements that collect light from the object and focus the image onto the sensor plane. Second is the camera hardware. For example, when using a charge coupled device (CCD) camera to acquire digital images, the incident illumination is converted into an electrical signal. The third component (which may be an integrated element in the hardware) is the digitization and storage process. Using an A/D device, the CCD signal is converted into an array of discrete digital intensity data. In this section, we apply the pinhole projection models from Chapter 2 and develop a formulation that includes (a) rigid body transformations between several coordinate systems used to represent various elements in the imaging process, (b) the transformation between image plane coordinates and skewed sensor coordinates and (c) the effect of distortion on image positions.

Michael A. Michael A., Jean-José Orteu, Hubert W. Schreier

4. Two-Dimensional and Three-Dimensional Computer Vision

Two-dimensional (2D) and three-dimensional (3D) computer vision employ the pinhole camera model, distortion models and general optimization procedures described in Chapter 3. For two-dimensional computer vision, it is assumed that the motions of a planar object occur within the object plane. In most 2D cases, the object plane is nominally parallel to the camera sensor plane. In 3D computer vision,1 the only restrictions placed on the motion of a curvilinear object are (a) the object remains in focus during the motion and (b) points of interest on the object are imaged onto two or more camera sensor planes. In the following sections, details regarding models and calibration procedures for 2D and 3D computer vision are provided.

Michael A. Michael A., Jean-José Orteu, Hubert W. Schreier

5. Digital Image Correlation (DIC)

Image matching is a discipline of computer vision that is of central importance to a large number of practical applications. To name just a few, image matching is used to solve problems in industrial process control, automatic license plate recognition in parking garages, biological growth phenomena, geological mapping, stereo vision, video compression and autonomous robots for space exploration. Since the applications are so varied, there are a wide variety of approaches and algorithms in use today, many specialized to a given task. For instance, highly specialized algorithms xist to determine motion vectors of small tracer particles used in the study of fluid flows. Digital image correlation is no exception, and algorithms are employed that take the physics of the underlying deformation processes into account. In one regard, however, digital image correlation is somewhat unique. Due to the miniscule motions that are often of interest in engineering applications, the resolution requirements are much higher than for most other applications. To accurately measure the stress-strain curve for many engineering materials, length changes on the order of 10?5 m/m have to be resolved. These requirements have led to the development of many algorithms targeted towards providing high resolution with minimal systematic errors.

This chapter discusses the fundamental problems in image matching with a focus on resolving the motions on the surface of deforming structures. Various fundamental concepts for digital image correlation are presented, and the most commonly used approaches are explored in detail.

Michael A. Michael A., Jean-José Orteu, Hubert W. Schreier

6. In-Plane Measurements

Two-dimensional deformation and motion measurements were the foundation of the early applications in digital image correlation for solid mechanics measurements. In all cases, a nominally flat specimen (with or without a geometric discontinuity) was imaged while being subjected to nominally tensile loading. Throughout the loading process, it was assumed that the specimen deformed within the original planar specimen surface.

Michael A. Michael A., Jean-José Orteu, Hubert W. Schreier

7. Stereo-vision System Applications

There are several initial considerations for a typical stereo-vision system, such as shown schematically in Fig. 4.3 or Fig. I.1. These include (a) anticipated object motion with corresponding (a-1) field of view on object, (a-2) system depth of field and (a-3) spatial resolution of camera; (b) surface lighting; (c) camera exposure time and (d) surface diffusivity.

Suppose the region of interest on the object is expected to move several millimetersto the right and then several millimeters towards one of the cameras during the loading process. If the stereo-vision system(s) are stationary, then the field of view for each camera must be arranged so that the final position of the object remains within the image for all cameras. Thus, both the depth of field and field of view for each camera-lens combination must be constructed to obtain a "focused imaging volume" that is appropriate for the situation. Assuming a fixed lens size, then the following are noted and shown schematically in Fig. 7.1.

Michael A. Michael A., Jean-José Orteu, Hubert W. Schreier

8. Volumetric Digital Image Correlation (VDIC)

In all of the previous sections, images of an object surface that are acquired by a sensor array are combined with a calibrated imaging model to convert the image sensor information into 2D or 3D surface position data. Typically, the imaging model is a form of perspective transformation, with functions defined to correct the model predictions.

In recent years, a series of advances in imaging, not only of surfaces but also for material volumes, have resulted in new opportunities for quantitative internal measurement of 3D positions throughout an entire volume. Computed Tomography (CT) scanners [26,27,30,155,156,188,265], Confocal Imaging Microscope architectures (CIM) [80] and Magnetic Resonance Imaging (MRI) [219,324,325] systems are examples of modern hardware that are now able to obtain and store massive amounts of digital volumetric image data, oftentimes exceeding the ability of the hardware or software to process and analyze the data.

Michael A. Michael A., Jean-José Orteu, Hubert W. Schreier

9. Error Estimation in Stereo-Vision

Error estimation in stereo-vision systems has been an area of research for many years [14, 59, 75, 81, 104, 124, 183, 228, 335]. The enclosed developments, based on the fundamental equations given in Chapters 3 and 4, are meant to provide an introduction to their application for estimation of both 3D position bias and variability. Consider a two-camera stereo vision system. As shown in Fig. 4.7, one point in space is in direct correspondence with two sensor locations, one in each camera system. Since the transformations between the world system and the camera 1 are known after calibration has been completed, it is assumed that the world coordinate system is transferred to the camera 1 pinhole location. Thus, if the common point is P, after the transformation is completed (a) the 3D coordinates are defined in the camera 1 system (e.g., see pinhole system in Fig. 3.1) and (b) the transformation given in Eq. (3.9) for the camera 1 view is greatly simplified, since [R]1 = [I] and {t}1 = {0}.

Michael A. Michael A., Jean-José Orteu, Hubert W. Schreier

10. Practical Considerations for Accurate Measurements with DIC

As shown in the several 2D examples in Chapter 6, the 3D examples in Chapter 7 and the volumetric imaging study in Chapter 8, digital image correlation has been used to make accurate measurements in a wide range of physically relevant experiments, ranging from the micro-scale to structural scale. As with any measurement method, effective use in laboratory or field conditions requires that the experimentalist exercise appropriate judgment when:

Selecting Lenses And Other Optical Components For Specific Experiments
Identifying And Employing Appropriate Digital Cameras
Configuring And Locating Each Component In The Imaging System
Arranging The Lighting Components
Determining The Appropriate Patterning Approach And Speckle Size
Choosing appropriate exposure time

In Section 10.1, practical suggestions regarding general imaging considerations are provided. These include (a) depth of field and field of view, (b) image artifacts that may affect measurement accuracy, (c) subset patterning and (d) exposure time. In Section 10.2, issues related to 2D-DIC measurements that are discussed include (e) out-of-plane motion (f) high magnification and depth of field and (g) measurement accuracy. In Section 10.3, issues related to 3D-DIC measurements that are discussed include (h) camera selection, (i) system configuration and specimen positioning, (j) calibration and (k) measurement accuracy.

Michael A. Michael A., Jean-José Orteu, Hubert W. Schreier

Backmatter

Titel: Image Correlation for Shape, Motion and Deformation Measurements
verfasst von: Hubert Schreier
Jean-José Orteu
Michael A. Sutton
Verlag: Springer US
Electronic ISBN: 978-0-387-78747-3
Print ISBN: 978-0-387-78746-6
DOI: https://doi.org/10.1007/978-0-387-78747-3

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