As in other machine vision applications, a good illumination and imaging system can reduce image processing requirements and increase reliability. Especially in three-dimensional machine vision, blurring due to either object or camera motion makes object location and recognition difficult. We examine the use of an electronic strobe light synchronized to an electronically shuttered CCD camera. Source design to reduce luminance variation with range for retroreflective materials is reviewed. Retroreflection greatly increases the luminance for near-axial sources and increases the effect of axial sources relative to ambient illumination.
As the technology in machine vision systems advances, the need for development of more effective illumination systems has become necessary. The result has been a dramatic increase in requests for both standard and custom-designed strobe illumination systems.
For a vision system to infer 3D object features (e.g., point features or line features) from 2D image features and to predict 2D image features from 3D object features, the transformation between the 2D image coordinate system and the 3D object coordinate system must be known. Determining this transformation is called (geometric) camera calibration. This 2D-3D transformation varies when the camera is moved by a robot. This paper presents a simple two-stage (off-line stage and on-line stage) method for calibrating a camera mounted on a robot. The off-line stage includes off-line calibration of the camera, the robot, and the robot-camera (or hand-eye) relation. The on-line stage can be divided into an initial calculation step and a re-calibration step. The initial step is computationally simple since it only involves one or two matrix multiplications of dimension less than four. The derived calibration accuracy from this initial step depends on the accuracy of the off-line camera/robot calibration. Experimental results show that the calibration accuracy is better than "1 part in 1000" without special robot calibration. Higher accuracy can be obtained with more sophisticated robot calibration, or with the re-calibration step using the extended Kalman filtering techniques. Some new insights to the conventional camera calibration methods are also given.
Lee's Time-to-Contact theory can be exploited to design simple, low-resolution optical sensors for robotics. An optical collision timer yields a direct measure of the safe time margin when approaching an object along the camera axis. This is achieved by timing the rate of image expansion ( looming ). This paper describes the Time-to-Contact paradigm, explores a family of architectures for coping with a variety of imaging conditions and concludes with a graphical simulation.
A new system will be presented that incorporates two electro-optical measurement components. An image processing unit in combination with a point sensor for the dynamical measurement of edge transitions. The integrated mechanical displacement system gives rise to the big measurement range while the optical sensor systems enable the measurement of complex workpieces with high precision.
Touch sensing arrays can provide information about both the magnitude and location of contact between a robotic gripper and an object in prehension. By providing a limited imaging capability, tactile arrays aid in evaluation of the state and progression of manipulative tasks. Most tactile arrays however have been built on rigid planar substrates and have therefore been limited to the provision of planar touch surfaces. For grippers of greater kinematic complexity than simple parallel jawed mechanisms, planar touch surfaces can limit the range of manipulative tasks that can be performed. A flexible touch sensor has been designed and constructed to allow tactile sensing over nonpianar surfaces. The sensor uses a force sensitive resistive polymer as the transductive medium. The polymer is deposited in row and column patterns on a thin flexible substrate, providing a low profile, nonrigid sensing device. The sensor operates as a resistance grid with an effective variable resistances between each row and column of the device. Each sensitive site is independently addressable and provides a resistance value that decreases exponentially with applied normal force. A set of 16 x 16 arrays has been built and tested and are currently in use as tactile sensors on Utah/MIT Dextrous Hand.
Solid state (CCD, CID, or multiplexed photosensor) television cameras are the most widely used input devices in machine vision, because they are relatively inexpensive, rugged, and reliable. However, the design, specification, and testing of these cameras typically are geared to their primary use in producing images that will ultimately be observed by humans; the intended applications for these cameras are as diverse as parking lot security and home entertainment. Because the video information produced by the camera is not used in the same ways by people and machine vision systems, there is no a priori reason to expect that a camera designed for one use will be optimal for another. In our work we have examined what makes a camera suitable for machine vision use. This paper describes which characteristics are important to the camera's performance machine vision applications and why. We show how these characteristics can be measured and standardized using simple tests suitable for production screening or more extensive tests suitable for use in the laboratory. Tests for important camera characteristics, including transfer function, noise, and resolution, are described and test results for representative solid state cameras are presented. Finally, we discuss how such measurements can be useful in designing or selecting the components of a machine vision system: the video capture systems, the cameras, and the image processing algorithms.
Automated optical inspection (A0I) technology has become vital in the printed wiring board (PWB) industry. AOI systems inspect automatically by scanning to acquire an image, processing the image to detect flaws, and displaying flaws to the operator for rework or rejection. AOI reduces costs by reducing scrap and improving yield. AOI systems pay for themselves by catching defects as early in the manufacturing process as possible: Before flawed artwork is used to print, before good layers are laminated with bad, before misdrilled boards are populated. The AOI-PWB industry places severe demands on optics technology. Features as small as six mils must be imaged clearly and registered exactly, and flaws as small as one mil can be fatal. We shall discuss how optics can be optimized for AOI;in particular, we shall explain the distinct advantages of fixed-focal length lenses over zoom lenses, and of custom lenses over general-purpose lenses.
The synthesis of minimum variance synthetic discriminant functions (MVSDF) for target detection in the presence of colored noise involves the invention of the noise correlation matrix. This may be numerically difficult even for low-resolution images. Methods must be found that allow synthesis of the MVSDF even when matrix inversion is not possible. We suggest an adaptive algorithm based on the well known LMS rule. Adaptive MVSDFs can maintain optimality in the presence of noise with unknown and non-stationary characteristics. The proposed adaptive synthesis technique "learns" characteristics of the noise source from sample realizations. This may seem as additional data and computation requirements, but comparable information and effort is necessary in the direct method to estimate the correlation matrix. The direct method (which uses the inverse of the correlation matrix) may be described as a two-step process, where the correlation matrix is determined in the first step and is used in the second step for the direct synthesis of the MVSDF. The proposed method iteratively converges on the optimum filter, and simultaneously gains knowledge about the noise source.
The method of using log-polar mapping with spectral band separation to form feature vectors for an associative memory is investigated. Log-polar mapping is used to provide the scale and rotation invariant properties. This reduces the teaching time and total capacity requirement for the associative memory because all orientations and sizes of the target object need not be learned. The images are also broken down into spatial frequency bands. The use of this technique is motivated by evidence that similar processes occur in the human visual system. Suspected benefits include enhanced recognition in the presence of noise and improved network robustness. Simulation results are presented for the case of character recognition.
A Ho-Kashyap (H-K) associative processor (AP) is demonstrated to have a larger storage capacity than the pseudoinverse AP and to allow linearly dependent key vectors to be accurately stored. A new Robust H-K AP is shown to perform well over all M/N (where M is the number of keys and N is their dimension), specifically when M ≈ N, where the standard pseudoinverse and H-K APs perform poorly. Also considered are variable thresholds, an error-correcting algorithm to allow analog synthesis of the H-K AP, and the different reliabilities of the recollection elements.
Path planning comprises a significant task in robot vision problems. The issue involves navigating from point A to B, avoiding obstacles on the way and satisfying other possible optimality criteria. In this context, obstacle avoidance forms the central part of the problem. Among the many path planning algorithms, multiresolution techniques based on hierarchical tree structures, e.g. quadtrees have shown great potential . The existing techniques, however, are offline, static algorithms that plan a path using a single quadtree. Such techniques are unable to cope with dynamic scenes where spatial occupancy may change. This work presents a technique whereby a quadtree-based spatial occupancy map is generated in real time, making an online path planning task feasible.
Pattern recognition filters that are invariant to image distortion, scale, rotation and structural noise have been demonstrated using the synthetic discriminant function (SDF) approach. A new method of developing invariant recognition filters based on the SDF and subspaces of the object space is developed. These filters are suggested as a technique to provide components for filters that contain contextual information. Demonstration of the technique using a simple example is provided.
Several optical processors using color information for product inspection are described. The systems described employ the use of inputs in different colors (RGB) to provide: enhancement of portions of the product, reduced noise, and improved contrast ratio for better optical Hough transform mensuration data. They also include a new frequency-multiplexed multi-color correlator and new and efficient techniques to employ only one or two wavelength sources in color procesng with a color liquid crystal television (LCTV). Real time optical laboratory data using an LCTV and thermoplastic light modulator are presented for optical Hough transform and correlation systems for product inspection. The color LCTV's phase distortion, contrast ratio and pixel size and the thermoplastic camera's parameters are quantified and analyzed.
Accurate grid labeling is a key step in recovering 3-D surfaces from structured light images. Knowledge of the real world (projector and camera geometry, surface continuity and smoothness, etc.) can be used to derive a set of local and global constraints which the grid labels must satisfy. Propagation of these constraints eliminates all but a small set of possible grid labels, but ambiguous solutions may still remain. This paper discusses a method of eliminating grid labeling ambiguity by adding constraints introduced by placing markers within the grid pattern. Grid labeling is based on geometric and topological constraints. Geometric constraints are global constraints on grid labels arising from knowledge of the camera and projector geometry, from assumed opaqueness of the object, and from knowledge of the work volume. Topological constraints are local constraints on grid labels arising from the sequential ordering of grid labels along a single grid stripe in the camera image, and from the assumption that a continuous (smooth) network of grid stripes in the camera image indicates a continuous (smooth) three-dimensional surface. This last assumption may be sometimes violated due to infrequent "viewing accidents" which may be caused by surface irregularities such as occluding contours or creases or by image processing errors. A problem with previous methods is the possible ambiguity of the recovered surface. This ambiguity occurs when more than one globally consistent set of grid labels is obtained, and consequently more than one object surface is possible. Our results show that the locations of the grid markers provide additional constraints to guide the grid labeling. We will present results of using several algorithms for labeling grids in structured light images. We will show that the additional constraints can be easily included into constraint propagation algorithms previously used for grid labeling.
This paper considers a technique for determining the true intersections of a ray with a cubicly-defined surface patch. To find all possible intersections of a ray and a surface patch, we apply an interval analysis, and implement ray tracing algorithm with Bezier surface patches.
It is now widely accepted that a certain class of naturally occurring textures are best modeled using the stochastic fractal methodologies proposed by Mandelbrot. Currently, most scene modeling techniques which appeal to the fractal paradigm construct their models by the successive application of perturbations to a primitive polygonally-based representation of the scene. While we concede the efficacy of this technique in rendering the model, we argue that the technique is inherently non-scale invariant, in that it requires that the perturbed model be recomputed whenever the viewpoint of the scene is altered. Rather than adopt this approach, we argue that a knowledge of the basic fractal statistics of the scene should be sufficient to construct a rendered model of the texture without requiring the intermediate computation of a perturbed polygonal structure. Our approach involves the application of fractal geometry to the illumination physics of the object; by this, we mean that a. basic (possibly polygonal) model of the object, along with its fractal statistics, will suffice to construct a rendered version of the object with a. fractal texture independent of scene viewpoint position. To accomplish this, we rely on local perturbations of illumination nornials at the time that the normal is evaluated from the basic model of the object. The extent and nature of this local perturbation is guided by both the fractal statistics of the object and the position of the scene viewpoint. Thus, we argue that the development of the stochastic texture be done in situ at the time that the illumination is developed, rather than performed as a preliminary step in the modeling of the scene. In this way, we substantially reduce the net computational complexity of the modeling process and its subsequent rendering, since the size of the ray-tree is determined by the complexity of the base object model and not the size of the perturbed and subdivided model.
Machine Vision and the field of Artificial Intelligence are both new technologies which have evolved mainly within the past decade with the growth of computers and microchips. And, although research continues, both have emerged from the experimental state to industrial reality. Today's machine vision systems are solving thousands of manufacturing problems in various industries, and the impact of Artificial Intelligence, and more specifically, the use of "Expert Systems" in industry is also being realized. This paper will examine how the two technologies can cross paths, and how an Expert System can become an important part of an overall machine vision solution. An actual example of a development of an Expert System that helps solve machine vision lighting and optics problems will be discussed. The lighting and optics Expert System was developed to assist the end user to configure the "Front End" of a vision system to help solve the overall machine vision problem more effectively, since lack of attention to lighting and optics has caused many failures of this technology. Other areas of machine vision technology where Expert Systems could apply will also be discussed.
This presentation will focus on the design and functional aspects of three-dimensional (3-D) imaging systems. AS a starting point performance characteristics will be discussed. These include: depth resolution and accuracy; lateral resolution, repeatability and accuracy; reflectance, sensitivity; working range; standoff; occlusion angle; and measurement rate. The performance of a given three-dimensional imaging systems will depend on the trade-offs made during the designing. process. Of course, some techniques are intrinsically better than others in certain performance areas. When classifying the various techniques for three-dimensional imaging they can be broken down into scanning and non-scanning approaches to producing full-field three-dimensional imagery. Systems that employ scanning include point triangulation and laser radar.. lion-scanning techniques include stereo imaging and moire, interferometry. The discussion of these techniques will focus on the strengths and weaknesses of each and the design considerations when building or using the technology.
Developing a range sensor for vehicle navigation within an unknown environment is a challenging problem. The combined requirements for a sensor's field of view, maximum range, and insensitivity to ambient light severely limit the potential speed and resolution of range sensors. In this paper, we describe a unique detector geometry used to implement a high speed, triangulation based line range sensor applicable to vehicle navigation scenarios. The range sensor derives its speed by simultaneously measuring off-axis angles to points along a target illuminated by a light stripe using an array of position sensitive detectors and an imaging lens. The position sensitivity of the array elements is derived from a unique triangular geometry designed to measure the lateral position of the light stripe image at high speed. We discuss the design, of the angle sensitive array and the line range system which uses the new detector geometry. In addition, we present experimental data generated from a range sensor based on this detector and show data from vehicle navigation experiments demonstrating the feasibility of this concept for mobile platform applications.
We have constructed a radar imaging system for simultaneous ranging and velocimetry of multiple points in the field of view. Signals are generated in an array of laser diodes in a compact, self-aligning, backscatter-modulation geometry. We present a theoretical model for signal generation in backscatter-modulated laser diodes, and describe a laboratory implementation used for finding the orientation and rotation speed of a object. The imaging radar could be used to enhance a variety of robot vision technologies, including object recognition with movement discrimination.
Active range finders based on triangulation have proven to be very useful when dense depth maps are required. A number of range finders utilize linear or bidimensional arrays of photodetectors (photodiodes or MOS-type) to provide depth information. A practical limitation of these sensors is their relatively low saturation level. Once the saturation exposure has been reached, the accuracy drops. Many applications require a 3-D sensor with a dynamic range in excess of 100 000:1. Most sensor arrays with position evaluation circuitry have a combined dynamic range of 100:1-1 000:1. Consequently, these 3-D sensors will have limited usefulness in these applications. Some practical considerations in this field are presented and the results are given which were obtained from a system, designed in-house, that controls the laser source in such a way that the saturation exposure on the sensor array is never exceeded. These preliminary results have demonstrated an increase of the dynamic range of the sensor by a minimum factor of 100. The maximum throughput rate is typically 100 000 depth measurements per second and can be as low as 300 per second.
One of the more prevalent applications of moire is contouring of parts. Some of the techniques available to generate contour data include phase shifting, fringe center mapping and frequency shifting. These techniques rely heavily on both extensive software analysis and rigorous hardware manipulation to produce different moire patterns of the same object. For example, frequency shifted moire requires that the grating frequency be changed in each of three of four successive images of the pattern. Phase shifted moire requires that the grating be changed in phase between successive images. This is done by physically moving the grating or moving it within software. In general, these techniques suffer from a lack of robustness. Taking multiple images with the hardware uses valuable time, during which the part may actually move and thereby distort the data. Any vibrations of the parts during data taking may also present a problem with extended amounts of inspection time. If the image is changed in the software, then the system can be fooled into interpreting reflectivity and illumination variations as moire pattern data. It is difficult to get a fast and accurate contour of a part in a real world environment with the present techniques available. There have, however, been advances in the video and machine vision industry that allow for the use of new tools, such as color. This paper describes work directed toward using color to improve existing contouring techniques. The goal is to develop a means to obtain a one time snapshot of the part under inspection that gives all of the necessary information required to produce a contour. This paper will address issues such as performance of color cameras, fabrication of color gratings, and use of a dichroic, multicamer'd system, contrasted with a multi-grating, multi-color illumination system.
An intensity ratio method for 3D imaging is proposed with error analysis given for assessment and future improvements. The method is cheap and reasonably fast as it requires no mechanical scanning or laborious correspondence computation. One drawback of the intensity ratio methods which hamper their widespread use is the undesirable change of image intensity. This is usually caused by the difference in reflection from different parts of an object surface and the automatic iris or gain control of the camera. In our method, gray-level patterns used include an uniform pattern, a staircase pattern and a sawtooth pattern to make the system more robust against errors in intensity ratio. 3D information of the surface points of an object can be derived from the intensity ratios of the images by triangulation. A reference back plane is put behind the object to monitor the change in image intensity. Errors due to camera calibration, projector calibration, variations in intensity, imperfection of the slides etc. are analyzed. Early experiments of the system using a newvicon CCTV camera with back plane intensity correction gives a mean-square range error of about 0.5 percent. Extensive analysis of various errors is expected to yield methods for improving the accuracy.
Active, laser based 3-D sensing techniques can provide several practical advantages for direct, real time depth measurement. Numerous active techniques exist ranging from camera based structured light used for object detection and height measurement through scanning laser radar systems targeted for complex tasks like robot navigation. In all systems the performance is limited by the level of optical and electronic noise in the system. This paper identifies the fundamental sources of optical and electronic noise and presents data which can be used to estimate the performance of several system configurations. The data is generally useful for improving the signal detection capability of many types of imaging systems. Implementation of noise reduction techniques can provide extraordinary optical and electronic dynamic range, particularly when laser scanning 3-D imaging systems are used.
A major hindrance to image segmentation tasks are the presence of specular highlights on object surfaces. Specular highlights appear on object surfaces where the specular component of reflection from illuminating light sources is so dominant that most detail of the object surface is obscured by a bright region of reflected light. Specular highlights are very common artifacts of most lighting environments and are not part of the intrinsic visible detail of an object surface. As a result, in addition to obscuring visible detail, specular highlight regions of an image can easily deceive image understanding algorithms into interpreting these regions as separate objects or regions on an object with high albedo. Recently, a couple of approaches to identifying specular highlight regions in images of object surfaces have produced some good results using color analysis. Unfortunately these methods work only for dielectric materials (e.g. plastic, rubber etc..) and require that the color of the object be different from the color of the light source. In this paper a technique is presented exploiting the polarization properties of reflected light to identify specular highlight regions. This technique works for both dielectric and metal surfaces regardless of the color of the illuminating light source, or the color detail on the object surface. In addition to separating out diffuse and specular components of reflection, the technique presented here also as a bonus can identify whether certain image regions correspond to a dielectric or metal object surface. Extensive experimentation will be presented for a variety of dielectric and metal surfaces, both polished and rough. Experimentation with coated surfaces using the technique presented here have not yet been studied.
Recently there has been interest, in computer vision research, in the segmentation of images based upon the actual material makeup of the objects or object parts that constitute image regions. The idea is to identify image characteristics which can be used to predict the material properties of objects that are being imaged. A majority of object surfaces can be simply classified according to their basic electrical properties; metal objects (e.g. Aluminum, Copper) conduct electricity rather well while dielectric objects (e.g. Rubber, Plastic, Ceramic) conduct electricity poorly. Distinguishing image regions according to whether they correspond to metal or dielectric material can provide important information for scene understanding especially in industrial machine vision. One such major application is circuit board inspection where the presence of dielectric or metal material in the wrong place can cause trouble. A previous approach to the problem of identifying metal or dielectric material in images is based upon careful spectral (i.e. color) analysis of reflected light from material objects. This paper presents a technique for identifying the material properties of objects in an image using a polarizing lens (i.e. Polaroid filter). Two images of the same scene are taken with a polarizing lens placed in front of a camera in two different respective orientations. Effectively these two images represent two linearly independent polarization components of the reflected light. It is shown that when the linearly independent components of polarization are taken parallel and perpendicular with respect to the plane in which specular rays travel that dielectric objects can be distinguished from metallic objects when specular highlights are present. In particular the two polarization components are very similar at specular highlights on metals while the two polarization components for specular highlights on dielectrics are very different, the perpendicular component having much larger magnitude than the parallel component. This is shown to hold regardless of whether the surface is polished or rough. Results for coated surfaces will be presented at a future date.
This paper deals with a new method of reconstructing 3D surfaces using some a-priori knowledge about them. The approach taken here uses the Shadowgram which relates shadows cast by the surface to the light source angle. Assuming that the contour of the surface can be described mathematically using a polynomial, the coefficients of the polynomial are evaluated using information from the Shadowgram.
We solve the stereo correspondence problem using Lapla-cian of Gaussian (LoG) zero-crossing contours as a source of primitives for structural stereopsis, as opposed to traditional point-based algorithms. For each image in the stereo pair, we apply the LoG operator, extract and link zero crossing points, filter and segment the contours into meaningful primitives, and compute a parametric structural description over the resulting primitive set. We then apply a variant of the inexact structural matching technique of Boyer and Kak Ill to recover the optimal interprimitive mapping (correspon-dence) function. Since an extended image feature conveys more information than a single point, its spatial and photometric behavior may be exploited to advantage; there are also fewer features to match, resulting in a smaller combinatorial problem. The structural approach allows greater use of spatial relational constraints, which allows us to eliminate (or reduce) the coarse-to-fine tracking of most point-based algorithms. Solving the correspondence problem at this level requires only an approximate probabilistic characterization of the image-to-image structural distortion, and does not require detailed knowledge of the epipolar geometry.
Conventional methods for the recovery of shape from shading assume homogeneity in the reflectance properties of the scene under analysis. However, imagery obtained from such sources as LANDSAT MSS or TM are usually comprised of regions of widely varying illumination characteristics. Given this, it follows that a single, non-partitioned approach to surface recovery from such images is almost always bound to fail. In this paper, we discuss a multifaceted approach to the problem of recovering surface features. We begin by classifying the image (through usual classificatory techniques) into distinct patches. For each of these surface types, a reflectance model is developed. This reflectance model is adjusted to coincide with the observed reflectance by the introduction of a reflectance remedy. This, in turn, leads to an image remedy equation. We then discuss an algorithm, which, under certain reasonable assumptions, will iteratively estimate the patch surface orientation, the reflectance remedy as well as the light source direction based on the equation developed.
The structured highlight inspection method uses an array of point sources to illuminate a specular object surface. The point sources are scanned and highlights on the object surface resulting from each source are used to derive local surface orientation information. The Extended Gaussian Image (EGI) is obtained by placing at each point on a Gaussian sphere a mass proportional to the area of points on the object surface that have a specific orientation. The EGI summarizes shape properties of the object surface and may be efficiently calculated from structured highlight data without surface reconstruction. Features of the estimated EGI including areas, moments, principal axes, homogeneity measures, and polygonality may be used as the basis for classification and inspection. The SHINY Structured Highlight INspection sYstem has been implemented using a hemisphere of 127 point sources. The SHINY system uses a binary coding scheme to make the scanning of point sources efficient. Experiments have used the SHINY system and EGI features for the inspection and classification of surface mounted solder joints. These experiments show excellent consistency with visual inspection and demonstrate the feasibility of the approach for production line inspection systems.
This paper proposes a method for determining the depth of points in a three-dimensional scene. The concept is to use two spheres with highly specular surfaces to obtain two different perspectives of the scene. Both spheres are viewed by a single stationary camera, and each sphere reflects the world around it into the camera. Correspondence between points on the two spheres is established by matching features such as edges and image intensities, as in traditional stereopsis. Depth is recovered from each pair of corresponding points by triangulation. The use of a single fixed camera avoids the undesirable complexities that characterize the stereo calibration procedure. The measurable range of the system is greatly enhanced by the use of specular spheres and is not limited by the field of view of the camera. Experiments were conducted to determine the accuracy in depth measurement and the feasibility of practical implementation. The technique presented in this paper has been named "SPHEREO" as it uses two SPHeres, rather than two cameras, to emulate stEREOpsis.
A new idea for the analysis of shape from reflectance maps is introduced in this paper. It is shown that local surface orientation and curvature constraints can be obtained at points on a smooth surface by computing the instantaneous rate of change of reflected scene radiance caused by angular variations in illumination geometry. The resulting instantaneous changes in image irradiance values across an optic sensing array of pixels constitute what is termed a photometric flow field. Unlike optic flow fields which are instantaneous changes in position across an optic array of pixels caused by relative motion, there is no correspondence problem with respect to obtaining the instantaneous change in image irradiance values between successive image frames. This is because the object and camera remain static relative to one another as the illumination geometry changes. There are a number of advantages to using photometric flow fields. One advantage is that local surface orientation and curvature at a point on a smooth surface can be uniquely determined by only slightly varying the incident orientation of an illuminator within a small local neighborhood about a specific incident orientation. Robot manipulators and rotation/positioning jigs can be accurately varied within small ranges of motion. Conventional implementation of photometric stereo requires the use of three vastly different incident orientations of an illuminator requiring either much calibration and/or gross and inaccurate robot arm motions. Another advantage of using photometric flow fields is the duality that exists between determining unknown local surface orientation from a known incident illuminator orientation and determining an unknown incident illuminator orientation from a known local surface orientation. The equations for photometric flow fields allow the quantitative determination of the incident orientation of an illuminator from an object having a known calibrated surface orientation. Computer simulations will be shown depicting photometric flow fields on a Lambertian sphere. Simulations will be shown depicting how photometric flow fields quantitatively determine local surface orientation from a known incident orientation of an illuminator as well as determining incident illuminator orientation from a known local surface orientation.