An introduction to digital image processing

An Introduction to Digital Image Processing Bill Silver Chief Technology Officer Cognex Corporation, Modular Vision Systems Division Digital image processing allows one to enhance image features of interest while attenuating detail irrelevant to a given application, and then extract useful information about the scene from the enhanced image This introduction is a practical guide to the challenges, and the hardware and algorithms used to meet them mages are produced by a variety of physical devices, including still and video cameras, x-ray devices, electron microscopes, radar, and ultrasound, and used for a variety of purposes, including entertainment, medical, business (e.g documents), industrial, military, civil (e.g traffic), security, and scientific The goal in each case is for an observer, human or machine, to extract useful information about the scene being imaged An example of an industrial application is shown in figure Often the raw image is not directly suitable for this purpose, and must be processed in some way Such processing is called image enhancement; processing by an observer to extract information is called image analysis Enhancement and analysis are distinguished by their output, images vs scene information, and by the challenges faced and methods employed Image enhancement has been done by chemical, optical, and electronic means, while analysis has been done mostly by humans and electronically I Digital image processing is a subset of the electronic domain wherein the image is converted to an array of small integers, called pixels, representing a physical quantity such as scene radiance, stored in a digital memory, and processed by computer or other digital hardware Digital image processing, either as enhancement for human observers or performing autonomous analysis, offers advantages in cost, speed, and flexibility, and with the rapidly falling price and rising performance of personal computers it has become the dominant method in use The Challenge An image is not a direct measurement of the properties of physical objects being viewed Rather it is a complex interaction among several physical processes: the intensity and distribution of illuminating radiation, the physics of Figure Digital image processing is used to verify that the correct tire is installed on vehicles at GM the interaction of the radiation with the matter comprising the scene, the geometry of projection of the reflected or transmitted radiation from dimensions to the dimensions of the image plane, and the electronic characteristics of the sensor Unlike for example writing a compiler, where an algorithm backed by formal theory exists for translating a high-level computer language to machine language, there is no algorithm and no comparable theory for extracting scene information of interest, such as the position or quality of an article of manufacture, from an image The challenge is often underappreciated by novice users due to the seeming effortlessness with which their own visual system extracts information from scenes Human vision is enormously more sophisticated than anything we can engineer at present and for the foreseeable future Thus one must be careful not to evaluate the difficulty of a digital image processing application on the basis of how it looks to humans Perhaps the first guiding principal is that humans are better at judgement and machines are better at measurement Thus determining the precise position and size of an automobile part on a conveyer, for example, is well-suited for digital image processing, whereas grading apples or wood is quite a bit more challenging (although not impossible) Along these lines image enhancement, which generally requires lots of numeric computation but little judgement, is well-suited for digital processing If teasing useful information out of the soup that is an image isn’t challenging enough, the problem is further complicated by often severe time budgets Few users care if a spreadsheet takes 300 milliseconds to update rather than 200, but most industrial applications, for example, must operate within hard constraints imposed by machine cycle times There are also many applications, such as ultrasound image enhancement, traffic monitoring, and camcorder stabilization, that require real-time processing of a video stream To make the speed challenge concrete, consider that the video stream from a standard monochrome video camera produces around 10 million pixels per second As of this writing the typical desktop PC can execute maybe 50 machine instructions in the 100 ns available to process each pixel The set of things one can in a mere 50 instructions is rather limited On top of this many digital image processing applications are constrained by severe cost targets Thus we often face the engineer’s dreaded triple curse, the need to design something good, fast, and cheap all at once Hardware Lights All image processing applications start with some form of illumination, typically light but more generally some form of energy In some cases ambient light must be used, but more typically the illumination can be designed for the application In such cases the battle is often won or lost right here—no amount of clever software can recover information that simply isn’t there due to poor illumination Generally one can choose illumination intensity, direction, spectrum (color), and continuous or strobed Intensity is easiest to choose and least important; any decent image processing algorithm should be immune to significant variations in contrast, although applications that demand photometric accuracy will require control and calibration of intensity Direction is harder to choose and more important, as any professional photographer knows The choices range from point sources at one extreme to “sky” illumination (equal intensity from every direction) at the other In between are various extended sources such as linear and ring lights The goal generally is to produce consistent appearance As a rule matte surfaces better with point sources and shiny, specularly-reflecting surfaces better with diffuse, extended sources A design that allows computer-controlled direction (usually by switching LEDs on and off) is often ideal Illumination color can sometimes be used as form of image enhancement Its primary value is that it’s cheap and adds zero processing time High speed image acquisition for rapidly moving or vibrating objects may require a strobe Most cameras have an electronic shutter which is preferable for low- to medium-speed acquisition, but as the exposure times get shorter the amount of light needed increases beyond what is reasonable to supply continuously Camera For our purposes a camera is any device that converts a pattern of radiated energy into a digital image stored in a random-access memory In the past this operation was divided into two pieces: conversion of energy to electrical signal, considered to be the camera’s function, and conversion and storage of the signal in digital form, performed by a digitizer As of this writing the distinction is becoming blurred, and before long cameras will feed directly to computer memory via USB, Ethernet, or IEEE 1394 interfaces Camera technology and the characteristics of the resulting images are driven almost exclusively by the highest volume applications, which until recently has been consumer television Thus most visible-light cameras in current use for digital image processing have resolution and speed characteristics established by TV broadcast standards almost a halfcentury ago As of this writing the typical visible light monochrome camera would have a resolution of 640 x 480 pixels, produce 30 frames per second, and support electronic shuttering and rapid reset (the ability to reset to the beginning of a frame at any time, to avoid having to wait before beginning an image acquisition) It would be based on CCD sensor technology, which produces good image quality but is expensive relative to most chips with a similar number of transistors Significantly higher resolution and speed devices are available but often prohibitively expensive An alternative is the line-scan camera, which uses a one-dimensional sensor and relies on scene motion to produce an image For the first time ever the landscape is changing, as high volume personal computer multimedia applications proliferate First affected were monitors, which for some time have offered higher-than-broadcast speed and resolution One can expect cameras to follow, with high-speed, high-resolution devices driven by consumer digital still camera technology and lower-resolution, ultra low cost units driven by entertainment, Internet conferencing, and perceptual user interface applications The low cost devices may have the greater influence These are based on emerging CMOS sensor technology, which uses the same process as most computer chips and is therefore inexpensive due simply to higher process volume Currently image quality is not up to CCD standards, but that is certain to change as the technology matures Although monochrome images have almost entirely disappeared in consumer applications, they still represent the majority in digital image processing due primarily to camera cost and data processing burden (for color those 50 instructions per pixel would drop to 17) Color cameras come in two forms: single sensor devices that alternate red, green, and blue pixels in some pattern, and much higher quality but more expensive devices with separate sensors for each color Monochrome pixels are usually bits (256 gray levels), although 10and 12-bit devices are sometimes used Video signals tend to be noisy, however, and careful engineering is required to get more than useful bits out of the signal Furthermore, robust image analysis algorithms not rely on photometric accuracy, so unless the application calls for accurate measurements of scene radiance, there is usually little or no benefit beyond bits Wide dynamic range is more useful than photometric accuracy, but it is usually best achieved by using a logarithmic response than by going to more bits Color pixels are 3-vectors (this is a fact of human physiology, not physics) Several representations, called color spaces, are commonly used for representing color The simplest to produce is the {red, green, blue} space (RGB), although {hue, intensity, saturation} (HIS) may be more useful for image analysis For the lower quality single-sensor cameras, the {luminance, chroma1, chroma2} space (YCC) is sometimes used Action Until recently the computational burden of digital image processing for the most part had to be handled by dedicated hardware Typically such hardware consisted of plug-in cards for PCI and/or VME backplanes, containing one or more applicationspecific integrated circuits (ASICs) designed for digital image processing The last few years has seen a move away from dedicated hardware towards pure software solutions, due to the advent first of DSPs and later general-purpose CPUs that fall at or above the billion operations per second mark Of these the most significant is the development of MMX processors by Intel Corporation MMX technology is well-suited for digital image processing Although it is hardly alone in being so, MMX is so widely available (all Intel-compatible PCs made since 1997) that it is the de facto standard for merchant digital image processing software This development is likely to solidify with the expected introduction sometime in 2000 on Merced processors of EPIC technology, jointly developed by Intel and Hewlett-Packard The EPIC architecture is superb for digital image processing The full power of the new processors is generally available only to skilled assembly language programmers, and this is unlikely to change in the foreseeable future Compiler vendors and the EPIC architects may argue otherwise, but direct experience in high-performance digital image processing has consistently shown this For timecritical applications, users should turn to specialists Algorithms We divide our discussion of digital image processing algorithms into image enhancement and image analysis The distinction is useful if not always clear-cut Generally image enhancement algorithms produce modified images as output, intended for subsequent analysis by humans or machines Their output behavior and execution speed are easy to characterize, and the basic algorithms are generally in the public domain Image analysis, by contrast, produces information that is much smaller in quantity but much more highly refined than an image, for example the position and orientation of an object In many cases the output is just an accept/reject decision, the smallest quantity of information but perhaps the highest refinement Output behavior and execution speed are generally difficult and sometimes impossible to characterize Image analysis algorithms are often a vendor’s most important intellectual property A simple example drawn from human experience will make these points concrete Imagine focusing a lens, which is an act of image enhancement It is easy to characterize what will happen (the picture gets sharper) and estimate how long it will take (a couple of seconds) The results will be fairly consistent from person to person, and there is no great secret as to how it’s done Now imagine that you are shown a picture of a specific car and asked to find it in a parking lot and report the space number This is image analysis If the lot is nearly empty then the results and time needed are easy to characterize and consistent If the lot is full, however, there is no telling how long it will take or even whether the correct answer will be reported, since many cars look alike Characterizing the output space number as a function of the input distribution of scene radiance measurements is essentially impossible Results may vary widely from person to person, and an individual’s “proprietary” methods may have a large bearing on the outcome The difficulty in characterizing the behavior of automated image analysis leads to a level of risk that is far greater than that of more typical software development projects, which are already notoriously risky The best ways to manage the risk are to rely on experienced professional developers, to share the risk between vendors and their clients, and to characterize performance empirically using a large database of stored images Image Enhancement Table shows a classification of digital image enhancement algorithms in common use The classification given is useful but neither complete nor unique The algorithms are broadly divided into two classes, point transforms and neighborhood operations Point transforms produce output images where each pixel is some function of a corresponding input pixel The function is the same for every pixel, and is often derived from global statistics of the image With neighborhood operations, each output pixel is a function of a set of corresponding input pixels This set is called a neighborhood because it is usually some region surrounding a corresponding center pixel, for example a 3x3 neighborhood Point transforms generally execute rapidly but are limited to global transformations such as adjusting overall image contrast Neighborhood operations can implement frequency and shape filtering and other sophisticated enhancements, but execute more slowly because the neighborhood must be recomputed for each output pixel Pixel mapping point transforms include a large set of enhancements that are useful with scalar-valued pixels (e.g monochrome images) Often these are implemented by a single software routine (or hardware module) that uses a lookup table Lookup tables are fast and can be programmed for any function, offering the ultimate in generality at reasonable speed MMX and similar processors, however, can perform a variety of functions much faster by direct computation than by table lookup, at a cost of increased software complexity TABLE IMAGE ENHANCEMENT ALGORITHMS Point transforms • pixel mapping − gain/offset control − histogram specification − thresholding • color space transforms • time averaging Pixel maps are most useful when the function is computed based on global statistics of the image One can process an image to have a desired gain and offset, for example, based on the mean and standard deviation, or alternatively, the minimum and maximum, of the input Histogram specification is a powerful pixel mapping point transform wherein an input image is processed so that it has the same distribution of pixel values as some reference image The pixel map for histogram specification is easily computed from histograms of the input and reference images Histogram specification is a useful enhancement prior to an analysis step whose goal is some sort of comparison between the input and the reference Thresholding is a commonly used enhancement whose goal is to segment an image into object and background A threshold value is computed above (or below) which pixels are considered “object” and below (or above) which “background” Sometimes two thresholds are used to specify a band of values that correspond to object pixels Thresholds can be fixed but are best computed from image statistics Thresholding can also be done using neighborhood operations In all cases the result is a binary image—only black and white are represented, with no shades of gray Thresholding has a long but checkered his tory in digital image processing Up until the mid 1980’s Neighborhood operations • linear filtering − smoothing − sharpening • boundary detection • non-linear filtering − median filter − morphology • re-sampling − resolution pyramids − coordinate transforms thresholding was a nearly universal first step in image analysis, due to the high cost of hardware needed to gray-scale processing As hardware cost dropped and sophisticated new algorithms were developed, thresholding became less important When thresholding works it can be quite effective, because it directly identifies objects against a background, and eliminates unimportant shading variation Unfortunately in most applications scene shading is such that objects cannot be separated from background by any threshold, and even when an appropriate threshold value exists in principal it is notoriously difficult to find it automatically Furthermore, thresholding destroys useful shading information and applies essentially infinite gain to noise at the threshold value, resulting in a significant loss of robustness and accuracy As a general rule, given the performance of modern processors and gray-scale image analysis algorithms, thresholding and image analysis algorithms that depend on thresholding are best avoided Color space conversion is used to convert between, for example, the RGB space provided by a camera to the HIS space needed by an image analysis algorithm Accurate color space conversion is computationally expensive, and often crude approximations are used in timecritical applications These can be quite effective, but it is a good idea to understand the tradeoffs between speed and accuracy before choosing an algorithm Time averaging is the most effective method of handling very low contrast images Pixel maps to increase image gain are of limited utility because they affect signal and noise equally Neighborhood operations can reduce noise but at the cost of some loss in image fidelity The only way to reduce noise without affecting the signal is to average multiple images over time The amplitude of uncorrelated noise is attenuated by the square root of the number of images averaged When time averaging is combined with a gain-amplifying pixel map, extremely low contrast scenes can be processed The principal disadvantage of time averaging is the time needed to acquire multiple images from a camera Linear filters are the best understood of the neighborhood operations, due to the extensively developed mathematical framework of signal theory dating back 200 years to Fourier Linear filters amplify or attenuate selected spatial frequencies, can achieve such effects as smoothing and sharpening., and usually form the basis of re-sampling and boundary detection algorithms Linear filters can be defined by a convolution operation, where output pixels are obtained by multiplying each neighborhood pixel by a corresponding element of a likeshaped set of values called a kernel, and then summing those products Figure 2a, for example, shows a rather noisy image of a cross within a circle Convolution with the smoothing (low pass) kernel of figure 2b produces figure 2c In this example the neighborhood is 25 pixels arranged in a 5x5 square Note how the highfrequency noise has been attenuated, but at a cost of some loss of edge sharpness Note also that the kernel elements sum to 1.0 for unity gain The smoothing kernel of figure 2b is a 2D Gaussian approximation The 2D Gaussian is among the most important functions used for linear filtering Its frequency response is also a Gaussian, which results in a well-defined passband and no ringing Kernels that approximate the difference of two Gaussians of different size make excellent band-pass and high-pass filters Figure 2d illustrates the effect of a band-pass filter based on a difference of Gaussian approximation using a 10x10 kernel Note that both the high frequency noise and the low frequency uniform regions have been attenuated, hardware than FFTs, is simpler to implement, and has little trouble with boundary conditions Boundary detection has an extensive history and literature, which ranges from simple edge detection to complex algorithms that might more properly be considered under image analysis We somewhat arbitrarily consider boundary detection under image enhancement because the goal is to emphasize features of interest (the boundaries) and attenuate 004 016 023 016 004 016 062 094 062 016 023 094 140 094 023 2e 062 016 016 062 094 004 016 023 016 004 2a 2b 2d 2c 2f Figure An image can be enhanced to reduce noise or emphasize boundaries leaving only the mid-frequency components of the edges Linear filters can be implemented by direct convolution or in the frequency domain using FFTs While frequency domain filtering is theoretically more efficient, in practice direct convolution is almost always preferred Convolution, with its use of small integers and sequential memory everything else The shading produced by an object in an image is among the least reliable of an object’s properties, since shading is a complex combination of illumination, surface properties, projection geometry, and sensor characteristics Image discontinuities, on the other hand, usually correspond directly to object surface Figure Image discontinuities usually correspond to physical object features, while shading is often unreliable addressing, is a better match for digital discontinuities (e.g edges), since the other factors tend not to be discontinuous Image discontinuities are generally consistent geometrically (i.e in shape) even when not consistent photometrically (see figure 3) Thus identifying and localizing discontinuities, which is the goal of boundary detection, is one of the most important digital image processing tasks Boundaries are usually defined to occur at points where the rate of change of image brightness is a local maximum, i.e at peaks of the first derivative or, equivalently, zerocrossings of the second derivative On a discrete grid such points can only be estimated, which can be done with linear filters designed to estimate first or second derivative The difference of Gaussian of figure 2d, for example, is a second derivative estimator, and boundaries show up as zero-crossings that occur at the sharp black-to-white transition points in the figure Figure 2e shows the output of a first derivative estimator, often called a gradient operator, applied to a noisefree version of figure 2a The gradient operator consists of a pair of linear filters designed to estimate first derivative horizontally and vertically, which gives components of the gradient vector The figure shows gradient magnitude, with boundaries defined to occur at the local magnitude peaks Crude edge detectors simply mark image pixels corresponding to gradient magnitude peaks or secondderivative zero-crossings Sophisticated boundary detectors produce organized chains of boundary points, with sub-pixel position and boundary orientation (accurate to a few degrees) at each point The best commercially available boundary detectors are also tunable in spatial frequency response over a wide range, and operate at high speed Non-linear filters designed to pass or block desired shapes rather than spatial frequencies have been found useful for digital image enhancement The first we consider is the median filter, whose output at each pixel is the median of the corresponding input neighborhood Roughly speaking the effect of a median filter is to attenuate image features smaller in size than the neighborhood and pass image features larger than the neighborhood Figure 2f shows the effect of a 3x3 median filter on the noisy image of figure 2a Note that the noise, which generally results in features smaller than 3x3 pixels, is strongly attenuated The basic morphology operations have many uses, one of which is shown in figure In the figure, the input image on the left is opened with a circular probe and a rectangular probe, resulting in the images shown on the right One might imagine the probe to be a paintbrush, with the output being everything the brush can paint while placed wherever in the Figure A morphology “opening” operation acts as a shape filter, whose behavior is controlled by a “probe” Unlike the linear smoothing filter of figure 2c, however, note that there is no significant loss in edge sharpness, since all of the cross and circle features are much larger than the neighborhood Thus a median filter is often superior to linear filters for noise reduction One of the main dis advantages of the median filter, however, is that it is very expensive to compute compared to linear filters, and the disparity gets worse as the neighborhood size increases Morphology refers to a broad class of non-linear shape filters Like the linear filters the operation is defined by a matrix of elements applied to input image neighborhoods, but instead of a sum of products, a minimum or maximum of sums is computed These operations are called erosion and dilation, and the matrix of elements is usually referred to as a probe rather than a kernel Erosion followed by a dilation using the same probe is called an opening, and dilation followed by erosion is called closing input it will fit (i.e entirely on black with no white showing) Notice how the opening operation with appropriate probes is able to pass certain shapes and block others For simplicity the example of figure illustrates opening as a binary (black/white) operation, but in general the morphology operations are defined on gray-level images, with the concept of probe fitting defined on 2D surfaces in 3-space Digital re-sampling refers to a process of estimating the image that would have resulted had the continuous distribution of energy falling on the sensor been sampled differently A different sampling, perhaps at a different resolution or orientation, is often useful One of the most important forms of digital re-sampling obtains a series of images at successively coarser resolution Such a series of images is called a resolution pyramid Conventionally each image in the series is half the resolution of the previous in each dimension (1/4 the number of pixels), but other choices are often preferable Resolution is reduced by a combination of low-pass filtering and sub-sampling (selecting every n th pixel) A resolution pyramid forms the basis of many image analysis algorithms that follow a coarse-to-fine strategy The coarse resolution images allow rough information to be extracted quickly, without being distracted and confused by fine and often irrelevant detail The algorithm proceeds to finer resolution images to localize and refine this information Another important class of resampling algorithms are coordinate transforms, which can shift by subpixel amounts, rotate and size images, and convert between Cartesian and polar representations Output pixel values are interpolated from a neighborhood of input values Three methods is common use are nearest neighbor, which is the fastest, bilinear interpolation, which is more accurate but slower and suffers some loss of high frequency components, and cubic convolution, which is very accurate but slowest Image Analysis It’s only a slight oversimplification to say that the fundamental problem of image analysis is pattern recognition, the purpose of which is to recognize image patterns corresponding to physical objects in the scene, and determine their pose (position, orientation, size, etc.) Often the results of pattern recognition are all that’s needed, for example a robot guidance system supplies an object’s pose to a robot, and in other cases a pattern recognition step is needed to find an object so that it can, for example, be ni spected for defects or correct assembly Pattern recognition is hard because a specific object can give rise to a wide variety of images depending on all of the factors previously discussed Furthermore, similar-looking objects may be present in the scene that must be ignored, and the speed and cost targets may be severe Blob analysis is one of the earliest methods widely used for industrial pattern recognition The premise is simple—classify image pixels as object or background by some means, join the classified pixels to make discrete objects using neighborhood connectivity rules, and compute various moments of the connected objects to determine object position (1st moments), size (0th moment), and orientation (principal axis of inertia, based on 2nd moments) The advantages of blob analysis include high speed, sub-pixel accuracy (in cases where the image is not subject to degradation), and the ability to tolerate and measure variations in orientation and size Disadvantages include inability to tolerate touching or overlapping objects, poor performance in the presence various forms of image degradation, inability to determine the orientation of certain shapes (e.g squares), and poor ability to discriminate amongst similarlooking objects Perhaps the most serious problem, however, is that in practice the only generally reliable method ever found for separating object from background was to arrange for the objects to be entirely brighter or entirely darker than the background This requirement so severely limits the range of potential applications that before long other methods for pattern recognition were developed Normalized correlation (NC) has been the dominant method for pattern recognition in industry over the last decade It is a member of a class of algorithms known as template matching, which starts with a training step wherein a picture of an object to be located (the template) is stored At run-time the template is compared to like-sized subsets of the image over a range of positions, with the position of greatest match taken to be the position of the object The degree of match (a numerical value) can be used for inspection, as can comparisons of individual pixels between the template and image at the position of best match NC is a gray-scale match function that uses no thresholds and ignores variation in overall pattern brightness and contrast It is ideal for use in template matching algorithms NC template matching overcomes many of the limitations of blob analysis —it can tolerate touching or overlapping objects, performs well in the presence of various forms of image degradation, and the NC match value is useful in some inspection applications Most significantly, perhaps, objects need not be separated from background by brightness, enabling a much wider range of applications Unfortunately, NC gives up some of the significant advantages of blob analysis, particularly the ability to tolerate and measure variations in orientation and size NC will tolerate small variations, typically a few degrees and a few percent (depending on the specific template), but even within this small range of orientation and size the accuracy of the results falls off rapidly These limitations have been partly overcome by using re-sampling methods to extend NC by rotating and scaling the templates so as to measure orientation and size These methods have been expensive, however, and by the time computer cost and performance made them practical they were superceded by the far superior geometric methods described below The Hough transform is a method for recognizing parametrically defined curves such as lines and arcs, as well as general patterns It starts with an edge detection step, which makes it more tolerant of local and non-linear shading variations than NC When used to find parameterized curves the Hough transform is quite effective; for general patterns NC may have a speed and accuracy advantage, as long as it can handle the shading variations Geometric pattern matching (GPM) is replacing NC template matching as the method of choice for industrial pattern recognition Template methods suffer from fundamental limitations imposed by the pixel grid nature of the template itself Translating, rotating, and sizing grids by non-integer amounts requires re-sampling, which is time consuming and of limited accuracy This limits the pose accuracy that can be achieved with template-based pattern recognition Pixel grids, furthermore, represent patterns using gray-scale shading, which as we’ve observed is often not reliable GPM avoids these limitations by representing an object as a geometric shape, independent of shading and not tied to a discrete grid Sophisticated boundary detection is used to turn the pixel grid produced by a camera into a conceptually real-valued geometric description that can be translated, rotated, and sized quickly and without loss of fidelity When combined with advanced pattern training and highspeed, high-accuracy pattern matching modules, the result is a truly general purpose pattern recognition and inspection method A well-designed GPM system should be as easy to train as NC template matching, yet offer rotation, size, and shading independence It should be robust under conditions of low contrast, noise, poor focus, and missing and unexpected features Pattern recognition time is application-specific, as is typical of image analysis methods For a ballpark figure, to locate a 150x150 pixel pattern in a 500x500 field of view with 360° orientation uncertainty might require 30 – 50 milliseconds on PCs current as of this writing Always test speed for a specific application, however, since times can vary considerably beyond any specified range GPM is capable of much higher pose accuracy than any templatebased method, as much as an order of magnitude better when orientation and size vary Table shows what can be achieved in practice when patterns are reasonably close to the training image in shape, and not too degraded Accuracy is generally higher for larger patterns; the example of table assumes a pattern in the 150x150 pixel range TABLE GEOMETRIC PATTERN MATCHING ACCURACY Translation ±0.025 pixels Rotation ±0.02 degrees Size ±0.05 percent GPM is also capable of providing detailed data on differences between a trained pattern and an object being inspected This difference data is also rotation, size, and shading independent Putting it All Together Often a complete digital image processing system combines many of the above image enhancement and analysis methods In the following example, the goal is to inspect objects by looking for differences in shading between an object and a pre-trained, defect-free example called a golden template Simply subtracting the template from an image and looking for differences does not work in practice, since the variation in gray-scale due to ordinary and acceptable conditions can be as great as that due to defects This is particularly true along edges, where slight (i.e subpixel) mis registration of template and image can give rise to large variation in grayscale Variation in illumination and surface reflectance can also give rise to differences that are not defects, as can noise A practical method of template comparison for inspection uses a combination of enhancement and analysis steps to distinguish shading variation due to defects from that due to ordinary conditions: A pattern recognition step (e.g GPM) determines the relative pose of the template and image A digital re-sampling step uses the pose to achieve precise alignment of template to image A pixel mapping step using histogram specification compensates for variations in illumination and surface reflectance The absolute difference of the template and image is computed A threshold is used to mark pixels that may correspond to defects Each pixel has a separate threshold, with pixels near edges having a higher threshold because their gray-scale is more uncertain A blob analysis or morphology step is used to identify those clusters of marked pixels that correspond to true defects Further Reading Digital image processing is a broad field with an extensive literature This introduction could only summarize some of the more important methods in common use, and may suffer from a bias towards industrial applications We have entirely ignored image compression, 3D reconstruction, motion, texture, and many other significant topics The following are suggested for further reading Ballard and Brown gives an excellent survey of the field, while the others provide more technical depth Ballard, D.H and Brown, C.M (1982) Computer Vision PrenticeHall, Englewood Cliffs, New Jersay Horn, B.K.P (1986) Robot Vision MIT Press, Cambridge, Massachusetts Pratt, W.K (1991) Digital Image Processing, 2nd Ed John Wiley & Sons, New York, NY Rosenfeld, A and Kak, A.C (1982) Digital Picture Processing, Vol and 2, 2nd Ed., Academic Press, Orlando, Florida COGNEX® Cognex Corporation One Vision Drive, Natick, MA 01760 Tel: (508) 650-3000 Fax: (508) 650-3333 Web: www.cognex.com Email: mktg@cognex.com © Copyright 2000, Cognex Corpration All rights reserved  ... between vendors and their clients, and to characterize performance empirically using a large database of stored images Image Enhancement Table shows a classification of digital image enhancement algorithms... of the image One can process an image to have a desired gain and offset, for example, based on the mean and standard deviation, or alternatively, the minimum and maximum, of the input Histogram... degradation), and the ability to tolerate and measure variations in orientation and size Disadvantages include inability to tolerate touching or overlapping objects, poor performance in the presence