Machine vision calibration targets and methods of determining their location and orientation in an image

A machine vision method analyzes a calibration target of the type having two or more regions, each having a "imageable characteristic," e.g., a different color, contrast, or brightness, from its neighboring region(s). Each region has at least two edges--referred to as "adjoining edges"--that are linear and that are directed toward and, optionally meet at, a reference point (e.g., the center of the target or some other location of interest). The method includes generating an image of the target, identifying in the image features corresponding to the adjoining edges, fitting lines to those edges, and determining the orientation and/or position of the target from those lines.

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to copyright protection. The owner thereof has no objection to facsimile 
reproduction by anyone of the patent document or the patent disclosure, as 
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BACKGROUND OF THE INVENTION 
The invention pertains to machine vision and, more particularly, to 
calibration targets and methods for determining their location and 
orientation in an image. 
Machine vision refers to the automated analysis of an image to determine 
characteristics of objects and other features shown in the image. It is 
often employed in automated manufacturing lines, where images of 
components are analyzed to determine placement and alignment prior to 
assembly. Machine vision is also used for quality assurance. For example, 
in the pharmaceutical and food packing industries, images of packages are 
analyzed to insure that product labels, lot numbers, "freshness" dates, 
and the like, are properly positioned and legible. 
In many machine vision applications, it is essential that an object whose 
image is to be analyzed include a calibration target. Often a cross-shaped 
symbol, the target facilitates determining the orientation and position of 
the object with respect to other features in the image. It also 
facilitates correlating coordinate positions in the image with those in 
the "real world," e.g., coordinate positions of a motion stage or conveyor 
belt on which the object is placed. A calibration target can also be used 
to facilitate determining the position and orientation of the camera with 
respect to the real world, as well as to facilitate determining the camera 
and lens parameters such as pixel size and lens distortion. 
In addition to cross-shaped marks, the prior art suggests the use of arrays 
of dots, bulls-eyes of concentric circles, and parallel stripes as 
calibration targets. Many of these targets have characteristics that make 
difficult finding their centers and orientations. This typically results 
from lack of clarity when the targets and, particularly, their borders are 
imaged. It also results from discrepancies in conventional machine vision 
techniques used to analyze such images. For example, the edges of a 
cross-shaped target may be imprecisely defined in an image, leading a 
machine vision analysis system to wrongly interpret the location of those 
edges and, hence, to misjudge the mark's center by a fraction of a pixel 
or more. By way of further example, a localized defect in a camera lens 
may cause a circular calibration mark to appear as an oval, thereby, 
causing the system to misjudge the image's true aspect ratio. 
In addition to the foregoing, many of the prior art calibration targets are 
useful only at a limited range of magnifications. Parallel stripes, for 
example, do not provide sufficient calibration information unless many of 
them appear in an image. To accommodate this, a machine vision system must 
utilize lower magnification. However, as the magnification decreases, so 
does the ability of the machine vision equipment to distinguish between 
individual stripes. Similar drawbacks limit the usefulness of the other 
prior art calibration targets for use in all but a narrow range of 
magnifications. 
Though the art suggests the use of checkerboard patterns as alignment 
marks, the manner in which images of those marks are analyzed by 
conventional machine systems also limits their utility to a limited range 
of magnifications. Particularly, prior art systems obtain alignment 
information from checkerboard marks by identifying and checking their 
corners, e.g., the eight black (or white) corners in a black-and-white 
image. By relying on corners, the systems necessitate that images show 
entire checkerboards, yet, with sufficient resolution to insure accurate 
detection and analysis. 
An object of this invention is to provide an improved calibration targets 
and methods for machine vision analysis thereof. 
A related object is to provide calibration targets and analysis methods 
reliable at a wide range of magnifications. 
A further object is to provide such methods as can be readily implemented 
on conventional digital data processors or other conventional machine 
vision analysis equipment. 
Yet still another object of the invention is to provide such methods that 
can rapidly analyze images of calibration target without undue consumption 
of resources. 
SUMMARY OF THE INVENTION 
The foregoing objects are among those attained by the invention, which 
provides in one aspect a machine vision method for analysis of a 
calibration target of the type having two or more regions, each having a 
different "imageable characteristic" (e.g., a different color, contrast, 
or brightness) from its neighboring region(s). Each region has at least 
two edges--referred to as "adjoining edges"--that are linear and that are 
directed toward and, optionally meet at, a reference point (e.g., the 
center of the target or some other location of interest). The method 
includes generating an image of the target, identifying in the image 
features corresponding to the adjoining edges, and determining the 
orientation and/or position of the target from those edges. 
In another aspect, the invention provides a method as described above for 
analyzing a target of the type that includes four regions, where the 
adjoining edges of each region are perpendicular to one another, and in 
which each region in the target has a different imageable characteristic 
from its edge-wise neighbor. The edges of those regions can meet, for 
example, at the center of the target, as in the case of a four-square 
checkerboard. 
In yet another aspect, the invention provides a method as described above 
for determining an orientation of the target as a function of the angle of 
the edges identified in the image and for determining the location of the 
reference point as an intersection of lines fitted to those edges. In 
regard to the former, the invention provides a method of determining the 
orientation of a target in an image by applying a Sobel edge tool to the 
image to generate a Sobel angle image, and by generating a angle histogram 
from that angle image. In an alternate embodiment, the orientation is 
determined by applying a Hough line tool to the image and determining the 
predominant angle of the edges identified by that tool. 
In regard to the location of the reference point, one aspect of the 
invention calls for locating the adjoining edges by applying a caliper 
vision tool to the image, beginning at an approximate location of the 
reference point. That approximate location of the reference point can 
itself be determined by applying a Hough line vision tool to the image in 
order to find lines approximating the adjoining edges and by determining 
an intersection of those lines. Alternatively, the approximate location of 
the reference point can be determined by performing a binary or grey scale 
correlation to find where a template representing the edges most closely 
matches the image. 
In another alternate embodiment, the approximate location of the reference 
point is determined by applying a projection vision tool to the image 
along each of the axes with which the adjoining edges align. A first 
difference operator vision tool and a peak detector vision tool are 
applied to the output of the projection tool (i.e., to the projection) in 
order to find the approximate location of the edges. 
The invention has wide application in industry and research applications. 
It facilitates the calibration of images by permitting accurate 
determination of target location and orientation, regardless of 
magnification. Thus, for example, an object bearing a target can be imaged 
by multiple cameras during the assembly process, with accurate 
determinations of location and orientation made from each such image. 
These and other aspects of the invention are evident in the drawings and in 
the description that follows.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENT 
FIGS. 1A-1C depict calibration targets according to the invention. 
Referring to FIG. 1A, there is shown a target 10 according to the 
invention having three regions 12, 14, 16. Each region is bounded by at 
least two linear edges that are oriented toward a reference location or 
reference point 18 on the target. Thus, for example, region 12 is bounded 
by edges 20, 24; region 14 is bounded by edges 20, 22; and region 16 is 
bounded by edges 22, 24. As evident in the drawings, the edges are shared 
by adjoining regions and, hence, are referred to below as "adjoining 
edges." Thus, region 12 shares edge 20 with region 14; region 14 shares 
edge 22 with region 16; and region 16 shares edge 24 with region 12. In 
the illustration, the reference point 14 is at the center of target 10, 
though, those skilled in the art will appreciate that the reference point 
can be positioned elsewhere. 
Each of the regions has a different imageable characteristic from its 
neighboring regions. As used herein, an "imageable characteristic" is a 
characteristic of a region as imaged by a machine vision system (e.g., of 
the type shown in FIG. 3) and, particularly, as imaged by an image capture 
device used by such a system. For example, in the illustration, region 12 
has the characteristic of being colored black; region 14, white; and 
region 16, gray. In addition to color, imageable characteristics useful 
with conventional machine vision systems--which typically utilize image 
capture devices operational in visual spectrum--include contrast, 
brightness, and stippling. 
Those skilled in the art will appreciate that any other characteristics by 
which a region may be identified and distinguished in an image are 
suitable for practice of the invention. Thus, for example, for a machine 
vision system that utilizes a temperature-sensitive (or infrared) image 
capture device, an imageable characteristic is temperature. By way of 
further example, for a machine vision system that utilizes a nuclear decay 
radiation-sensitive image capture device, an imageable characteristic is 
emitted radiation intensity or frequency. 
As shown in the illustration, the adjoining edges 20, 22, 24 comprise 
straight linear segments. Those edges are implicitly defined as the 
borders between regions that, themselves, have different imageable 
characteristics. Thus, for example, edge 20 is a straight linear segment 
defined by the border between black region 12 and white region 14. 
Likewise, edge 24 is defined by the border between black region 12 and 
gray region 16. Further, edge 22 is defined by the border between white 
region 14 and grey region 16. 
FIG. 1B depicts a calibration target 30 according to the invention having 
four rectangular (and, more particularly, square) regions 32, 34, 36, 38. 
As above, each region is bounded by at least two linear edges that are 
oriented toward a reference point 40 at the center of the target. Thus, 
for example, region 32 is bounded by edges 42, 44; region 34 is bounded by 
edges 42, 46; and so forth. As above, these edges are shared by adjoining 
regions. Thus, region 32 shares edge 42 with region 34, and so forth. Each 
region in target 30 has a different imageable characteristic from its 
edge-wise neighbor. Hence, regions 32 and 36 are white, while their 
edge-wise adjoining neighbors 34, 38 are black. 
FIG. 1C depicts a calibration target 50 according to the invention having 
five regions 52, 54, 56, 58, 60, each having two linear edges directed 
toward a reference point 62. The adjoining regions are of differing 
contrast, thereby, defining edges at their common borders, as illustrated. 
Although the edges separating the regions 52-60 of target. 50 are directed 
toward the reference point 62, they do not meet at that location. As 
evident in FIG. 1C, no marker or other element imageable characteristic is 
provided at reference point 62. 
Those skilled in the art will appreciate that, in addition to the 
calibration targets shown in FIGS. 1A-1C, targets with still more regions 
(or as few as two regions) and shapes, otherwise in accord with the 
teachings hereof, fall within the scope of the invention. Moreover, it 
will be appreciated that targets may be of any size and that their regions 
need not be of uniform size. Still further, it will be appreciated that 
the outer borders of the targets need not be linear and may, indeed, take 
on any shape. 
FIG. 2 depicts an object according to the invention for use in machine 
vision imaging, detection, and/or manipulation having a calibration target 
according to the invention coupled thereto. In the illustration, the 
object is an integrated circuit chip 70 having coupled to the casing 
thereof a calibration target 72 of the type shown in FIG. 1B. Other 
targets according to the invention, of course, can likewise be coupled to 
the object 70. The targets can be coupled to the object by any known 
means. For example, they can be molded onto, etched into, or printed on 
the surface of the object. By way of further example, decals embodying the 
targets can be glued, screwed or otherwise affixed to the object. 
Moreover, by way of still further example, calibration plates 
incorporating the targets can be placed on the object and held in place by 
friction. In addition to integrated circuit chips, the object can include 
any other objects to which a target can be coupled, such as printed 
circuit boards, electrical components, mechanical parts, containers, 
bottles, automotive parts, paper goods, etc. 
FIG. 3 depicts a machine vision system 80 according to the invention for 
determining the reference point and orientation of an object 82 having 
coupled thereto a calibration target 84 according to the invention and, 
particularly, a four-region target of the type shown in FIG. 1B. The 
system 80 includes an image capture device 86 that generates an image of a 
scene including object 82. Although the device may be responsive to the 
visual spectrum, e.g., a conventional video camera or scanner, it may also 
be responsive to emissions (or reflections) in other spectra, e.g., 
infrared, gamma-ray, etc. Digital image data (or pixels) generated by the 
capturing device 86 represent, in the conventional manner, the image 
intensity (e.g., contrast, color, brightness) of each point in the field 
of view of the capturing device. 
That digital image data is transmitted from capturing device 86 via a 
communications path 88 to an image analysis system 90. This can be a 
conventional digital data processor, or a vision processing system of the 
type commercially available from the assignee hereof, Cognex Corporation, 
as programmed in accord with the teachings hereof to determine the 
reference point and orientation of a target image. The image analysis 
system 90 may have one or more central processing units 92, main memory 
94, input-output system 96, and disk drive (or other mass storage device) 
98, all of the conventional type. 
The system 90 and, more particularly, central processing unit 92, is 
configured by programming instructions according to teachings hereof for 
operation as illustrated in FIG. 4 and described below. Those skilled in 
the art will appreciate that, in addition to implementation on a 
programmable digital data processor, the methods and apparatus taught 
herein can be implemented in special purpose hardware. 
Referring to FIG. 4 there is shown a machine methodology according to the 
invention for interpreting an image of a target 84 to determine its 
reference point and orientation. The discussion that follows is 
particularly directed to identifying a four-region target of the type 
shown in FIG. 1B. Those skilled in the art will appreciate that these 
teachings can be readily applied to finding targets according to the 
invention, as well as to other targets having detectable linear edges that 
are oriented toward a reference location or reference point on the target, 
e.g., a prior art cross-shaped target. For convenience, in the discussion 
that follows, such linear edges are referred to as "adjoining edges," 
regardless of whether they are from calibration targets according to the 
invention or from prior art calibration targets. 
In step 100, an image of the target 84 (or of the target 84 and object 82) 
is generated, e.g., using image capture device 86, and input for machine 
vision analysis as discussed below. The image can be generated real time, 
retrieved from a storage device (such as storage device 98), or received 
from any other source. 
In steps 102-108, the method estimates the orientation of the target in the 
image using any of many alternative strategies. For example, as shown in 
step 102, the method determines the orientation by applying a conventional 
Hough line vision tool that finds the angle of edges discernable in the 
image. In instances where the target occupies the entire image, those 
lines will necessarily correspond to the adjoining edges. Where, on the 
other hand, the target occupies only a portion of the image, extraneous 
edges (e.g., from other targets) may be evident in the output of that 
tool. Although those extraneous edges can generally be ignored, in 
instances where they skew the results, the image can be windowed so that 
the Hough vision tool is only applied to that portion that contains the 
target. Once the angles of the lines has been determined by the Hough line 
tool, the orientation of the image is determined from the predominant ones 
of those angles. Alternatively, the angle of the image can be determined 
by taking a histogram of the angles. 
The Hough vision tool used in step 102 may be of the conventional type 
known and commercially available for finding the angle of lines in image. 
A preferred such tool is the Cognex Line Finder, commercially available 
from the Assignee hereof, Cognex Corporation. A further discussion of that 
preferred tool is provided in the Appendix filed herewith. 
An alternative to using a Hough vision tool is shown in step 106. There, 
the illustrated method determines the orientation of the target by 
applying a Sobel edge tool to the image to find the adjoining edges. 
Particularly, that tool generates a Sobel angle image that reveals the 
direction of edges in the image. As above, where the target occupies the 
entire image, the adjoining edges will be the only ones discerned by the 
Sobel edge tool image. Where, on the other hand, the target occupies only 
a portion of the image, any extraneous edges can be ignored or windowed 
out. 
The Sobel edge tool may be of the conventional type known and commercially 
available for finding lines in image. A preferred such tool is the Cognex 
Edge Detection tool, commercially available from the Assignee hereof, 
Cognex Corporation. A further discussion of that preferred tool is 
provided in the Appendix filed herewith. 
Once the Sobel angle image is generated, in step 106, the orientation of 
the target in the image is determined by generating a histogram of the 
edge angle information; see, step 108. From that histogram, the target 
orientation can be determined by taking a one-dimensional correlation of 
that histogram with respect to a template histogram of a target oriented 
at 0.degree.. Where a Sobel magnitude image is generated, in addition to 
the Sobel angle image, such a histogram can be generated by counting the 
number of edges greater then a threshold length at each orientation. 
As a still further alternative to applying a Hough vision tool or Sobel 
edge tool, the method contemplates obtaining the angle of orientation of 
the target from the user (or operator). To this end, the user may enter 
angle orientation information via a keyboard or other input device coupled 
with digital data processor 90. 
In steps 110-118, the method determines the location, i.e., coordinates, of 
the target reference point in the image. Particularly, in step 110, the 
method can apply a Hough vision tool, as described above, to find the 
angle of lines discernable in the image. A conventional Hough vision tool 
determines, in addition to the angle of lines in an image, the distance of 
each line, e.g., from a central pixel. As above, where the target occupies 
the entire image, those lines will be the only ones discernable by the 
Sobel edge tool image. Where, on the other hand, the target occupies only 
a portion of the image, any extraneous edges can be ignored or windowed 
out. 
As above, the Hough vision tool used in step 104 may be of the conventional 
type known and commercially available for finding the angle and position 
of lines in image. Once again, a preferred such tool is the Cognex Line 
Finder, commercially available from the Assignee hereof, Cognex 
Corporation. A further discussion of that preferred tool is provided in 
the Appendix filed herewith. Those skilled in the art will, of course, 
appreciate that steps 102 and 110 can be combined, such that a single 
application of the Hough vision tool provides sufficient information from 
which to determine both the orientation of the target in the image and its 
reference point. 
As an alternative to using a Hough vision tool, the method can apply a 
projection vision tool to the image in order to find the position of the 
lines discernable in the image; see, step 112. The projection tool, which 
maps the two-dimensional image of the target into a one-dimensional image, 
is applied along the axes defined by the edges in the image. As those 
skilled in the art will appreciate, the location of the edges can be 
discerned from by finding the peaks in the first derivatives of each of 
those projections. As above, where the target occupies the entire image, 
those lines will be the only lines discernable by the Sobel edge tool 
image. Where, on the other hand, the target occupies only a portion of the 
image, any extraneous edges can be ignored or windowed out. 
The projection vision tool used in step 112 may be of the conventional type 
known and commercially available for mapping a two-dimensional image of 
the target into a one-dimensional image. A preferred such tool is that 
provided with the Cognex Caliper tool commercially available from the 
Assignee hereof, Cognex Corporation. A further discussion of that 
preferred tool is provided in the Appendix filed herewith. 
In step 114, the method uses the information generated in steps 110 and 112 
to compute the location of the reference point, particularly, as the 
intersection of the lines found in those steps 110 and 112. 
As an alternative to using the Hough vision tool and the projection tool, 
the method can apply determine the location of the reference point by 
performing a binary or grey scale correlation on the image; see step 116. 
To this end, the method uses, as a template, a pattern matching the 
expected arrangement of the sought-after edges, to wit, a cross-shaped 
pattern in the case of a target of the type shown in FIG. 1B. The use of 
correlation vision tools for this purpose is well known in the art. The 
template for such an operation is preferably generated artificially, 
although it can be generated from prior images of similar targets. 
As still another alternate to the Hough vision tool and the projection 
tool, the method can apply a grey-scale image registration using the sum 
of absolute differences metric between the image and a template; see step 
118. To this end, the method uses, as a template, a pattern matching the 
expected arrangement of the sought-after edges, to wit, a cross-shaped 
pattern in the case of a target of the type shown in FIG. 1B. The template 
for such an operation is preferably generated artificially, although it 
can be generated from prior images of similar targets. A preferred 
grey-scale image registration tool is disclosed in U.S. Pat. No. 
5,548,326, the teachings of which are incorporated herein by reference. 
Although steps 110-118 can be used to determine the approximate location of 
the reference point of the target in the image, the method utilizes 
optional steps 120 and 122 to refine that estimate. These two steps are 
invoked one or more times (if at all) in order make that refinement. 
In step 120, the method applies a conventional caliper vision tool to find 
points in the image that define the adjoining edges of the regions. On the 
first invocation of step 120, the method applies calipers along fifty 
points along each edge (though those skilled in the art will appreciate 
that other numbers of points can be used), beginning with points closest 
to the estimate of the reference point, as discerned in steps 110-118. The 
calipers are preferably applied a small distance away from the actual 
estimate of the reference point to avoid skewing the analysis due to 
possible misprinting of the target at that point, a missing pattern at 
that point (e.g., FIG. 1C), or a too-high spatial frequency at that point 
(e.g., FIG. 1B). In step 120, the method then fits a line to the points 
found along each edge by the caliper tool, preferably, using a 
conventional least squares technique. 
In step 122, the method computes a refined location of the reference point 
as the intersection of the lines identified in step 120. Although 
conventional geometric calculations can be performed for this purpose, 
preferably, the reference point is computed using conventional least 
squares techniques. Preferably, when examining the image of a symmetric 
calibration target of the type shown in FIG. 1B, the method utilizes the 
same number of points on either side of (and closest to) the reference 
point for purposes of fitting each line. This minimizes the bias otherwise 
introduced by a conventional edge detection technique in finding edges 
that are defined only by dark-to-light (or light-to-dark) transitions. 
Calibration targets of the type shown in FIG. 1B are advantageously 
processed by a method according to the invention insofar as they further 
minimize bias otherwise introduced by a conventional edge detection 
techniques. In this regard, it will be appreciated that such bias is 
reduced by the fact that "opposing" adjoining edges (i.e., edges that 
oppose one another across the reference point) define straight linear 
segments that change polarity across the reference point. That is, those 
segments are defined by regions that transition--preferably, equally in 
magnitude--from light-to-dark one one side of the reference point, and 
from dark-to-light on the other side. This is true for all "symmetric" 
calibration targets according to the invention, i.e., targets in which 
opposing edges define straight linear segments that are opposite polarity 
on either side of the reference point. 
On the second and subsequent invocations of step 120, the method 
specifically applies the caliper tool at points along the lines found in 
the previous iteration. Preferably, these points are at every pixel in the 
image that lies along the line, though, those skilled in the art will 
appreciate that few points can be used. The calipers can be applied 
orthogonal to the lines, though, in the preferred embodiment, they are 
applied along the grid defined by the image pixels. The caliper range 
decreases with each subsequent invocation of step 120. The method 
continues applying the calipers, beginning at the estimated center point 
until one of the four following situations occurs: no edge is found by the 
caliper applied at the sample point; more than one edge is found by the 
caliper and the highest scoring edge is less than twice the score of the 
second highest scoring edge (this 2.times. comes from the CONFUSION.sub.-- 
THRESHOLD); the distance between a computed edge point and the nominal 
line (computed from the previous invocation of step 120) is larger than a 
threshold (which threshold decreases with each subsequent invocation of 
step 120); or, the caliper extends outside of the image. As above, in step 
120, the method then fits a line to the points found along each edge by 
the caliper tool, preferably, using a conventional least squares 
technique. 
In the second and subsequent invocations of step 122, the method computes a 
refined location of the reference point as the intersection of the lines 
identified in step 120. As above, although conventional geometric 
calculations can be performed for this purpose, preferably, the reference 
point is computed using conventional least squares techniques. 
Referring to FIG. 5, there is also shown a machine methodology according to 
the invention for interpreting an image of a target 84 to determine its 
reference point and orientation. Particularly, in step 150, the method 
calls for generating an image of a target 84 and, particularly, of a 
target according to the invention having two or more regions, each region 
being defined by at least two linear edges that are directed toward a 
reference point, and having at least one of the regions having a different 
imageable characteristic from an adjacent region. Step 152 can be effected 
in the manner described in connection with step 100 of FIG. 4, or 
equivalents thereof. 
In step 152, the method analyzes the image to generate an estimate of an 
orientation of the target in the image. Step 152 can be effected in the 
manner described in connection with steps 102-108 of FIG. 4, or 
equivalents thereof. 
In step 154, the method analyzes the image to generate estimate of a 
location of the target's reference point. Step 154 can be effected in the 
manner described in connection with steps 110-118 of FIG. 4, or 
equivalents thereof. 
In step 156, the method analyzes the image to refine its estimates of the 
location of the reference point in the image and the orientation of the 
target in the image. Step 156 can be effected in the manner described in 
connection with steps 120-122 of FIG. 4, or equivalents thereof. 
Calibration target and methods for analysis according to the invention are 
advantageous over prior art targets and methods insofar as they are 
magnification invariant. By analyzing the adjoining edges of targets, 
methods according to the invention insure reliance on features (to wit, 
regions) that retain the same imageable appearance regardless of 
magnification. This is in contrast to prior art targets and methods, which 
rely on individual lines (or dots) to define calibrating features. As 
noted above, the imaging appearances of such lines and dots change with 
varying degrees of magnification. Even the prior art methods that analyze 
checkerboard targets rely on analysis of corners, which are not 
magnification invariant. 
The magnification invariance of targets and methods according to the 
present invention is illustrated in FIGS. 6A-6C. Referring to FIG. 6A, 
there is shown an imaging setup wherein camera 200 images a target 202 (on 
object 204) from a height x. An image generated by camera 200 is displayed 
on monitor 206 of workstation 208. Referring to FIG. 6B, there is shown an 
identical imaging setup, except insofar as a camera (of identical 
magnification) images a target (of identical size) from a greater height, 
x'. Likewise, FIG. 6C shows an identical imaging setup, except insofar as 
a camera (again, of identical magnification) images a target (again, of 
identical size) from a still greater height, x". Comparing monitor images 
depicted in FIGS. 6A-6C, it is seen that the images of the targets, 
generated by the cameras and displayed on the monitors, are identical in 
appearance regardless of the relative heights (x, x', and x") of the 
camera. This magnfication invariance results from the fact that the target 
has the same appearance regardless of height (or equivalently, 
magnification), within specified limits thereof. Those skilled in the art 
will appreciate that those limits are greater than the analagous limits 
for prior art targets (e.g., cross hairs, parallel stripes, etc.). 
Still another advantage of calibration targets and methods according to the 
invention is that they permits angular orientation to be determined 
throughout a full 360.degree. range. With reference to FIG. 1D, for 
example, the relative positions of the regions can be used to determine 
the overall orientation of the target, i.e., whether it is rotated 
0.degree., 90.degree., 180.degree., or 270.degree.. This information can 
be combined with a determination of relative orientation made by analysis 
of the adjoining edges as discussed above to determine the precise 
position of the target. 
A further understanding of the operation of an embodiment of the invention 
may be attained by reference to the Appendix hereto, providing a software 
listing of a preferred machine vision methodology for analyzing an image 
containing a target. 
Described herein are calibration targets and methods for determining the 
location and orientation thereof meeting the objects set forth above. It 
will be appreciated that the embodiments shown in the drawings and 
discussed above are merely illustrative of the invention, and that other 
embodiments incorporating changes therein fall within the scope of the 
invention, of which