Abstract:
Methods and apparatuses are disclosed for refining groupings of edge points that represent contours in an image. The methods and apparatuses decrease data dispersion and data quantization effects. The methods and apparatuses are particularly useful for accurate and robust detection of straight line-segment features contained in noisy, cluttered imagery occurring in industrial machine vision applications. Additionally, a measurement criterion of the quality of the detected line segments is introduced.

Description:
This application claims the benefit of U.S. Provisional Application No. 60/131,932, filed Apr. 30, 1999. 

   FIELD 
   This invention relates to machine vision, and particularly to methods and apparatuses for interpretation of edge point data from an image. 
   BACKGROUND 
   Dispersion of data is a common problem in many fields, including image processing. In image processing, data fails to converge to one grouping for numerous reasons, such as, imperfections in the imaging environment, the algorithm(s) employed, and/or the discrete nature of processing the data using a computer. Data dispersion detrimentally affects some types of image processing more than others. For instance, finding lines in images is more detrimentally effected by dispersion than finding regions. Typically, the integrity of smaller groupings of data, such as lines, relative to the remainder of the image, suffer more from dispersion effects. It is also difficult to identify elements composed of a relatively small amount of data because of confusing appropriate data with superfluous data. 
   An example of dispersion of edge points of a line is illustrated using  FIG. 1 , not drawn to scale, which depicts an imaged line  102  having multiple edge-point directions  100 , shown schematically. An edge point is derived from underlying image pixels, where an image pixel is a picture element characterized by a grey value, where an image can be represented as an array of image pixels. A plurality of connected edge points creates a contour, such as a line or boundary  200  between two regions  202  and  204 , illustrated in FIG.  2 . The direction of an edge point  210  is perpendicular to the line  200  upon which the edge point  208  resides. Turning back to  FIG. 1 , the edge points  110  of the line  102  do not share a common direction  100 , but are distributed about a peak angle, as shown in the discrete-angle histogram  104 . The edge-point directions  100  fall into multiple discrete bins  108  that are distributed around a peak bin  106 , where the peak bin  106  represents the mode of the histogram (i.e. the primary direction of the edge points  1   10  in the line  102 ). The lack of convergence of all the edge points  110  to the peak bin  106  illustrates the typical data dispersion present for lines in images. Lines detected using the Hough line-transform method also suffer from this problem. 
   The majority of line finding algorithms in machine-vision applications, are variations of the Hough line-transform method, described in U.S. Pat. No. 3,069,654. The Hough line-transform method transforms characteristics of edge points into line characteristics, and represents the line characteristics on a Hough space, where a point in the Hough space represents a line. 
   The characteristics of the edge points include the edge-point position, denoted (x, y), edge-point direction, denoted θ, and optionally, edge-point magnitude, denoted M, which are all measured in Cartesian space. The edge-point position is typically a function of the position of a neighborhood of the underlying image pixels. The edge-point magnitude and direction are a function of the change in grey value of the image pixels that contribute to the edge point. 
   The characteristics of an edge point, (θ, x, y, and optionally M) are transformed into line characteristics (d, c, and α) Typically, the characteristics of edge points in a contour are called features (such as position), while characteristics derived from the features are called parameters (such as line angle). 
   The line characteristics are illustrated in Cartesian space in FIG.  3 . The line characteristics include a line angle  302 , denoted α, which is the angle of the line  300  from the horizontal, a distance-vector  304 , denoted d, which is the shortest distance from the origin of a coordinate system  314  to the line  300 , and, optionally, a collinear distance  306 , denoted c, which is the distance from the edge point  308  to the place where d touches the line  300 , in Cartesian space. d is signed to differentiate between lines with identical α and d parameters on opposite sides of the origin  314 . More specifically, the sign of d is negative if the angle  312  of d from the horizontal in Cartesian coordinates is less than 180° and greater than, or equal to, zero (i.e., 180°&gt;β≧0); and positive when the angle  312  of d is less than 360°, and greater than, or equal to, 180° (i.e., 360°&gt;β≧180°). 
   d, c, and α are generated from the following Hough-transform equations:
 
 d=x ·sin(θ)− y ·cos(θ)  [1]
 
 c=x ·cos(θ)+ y ·sin(θ)  [2]
 
α degrees =[θ+90] mod180   [3]
 
d and α are stored on a Hough space.
 
     FIG. 4A  depicts an instance of a Hough space  400  for lines. The Hough space for lines is a two-dimensional space in which lines from an image are recorded. The Hough space is adequately represented as a two-dimensional array of bins  402 . One axis  404  represents the line-angle, α, and the other axis  406  represents the distance vectors, d. A point on a Hough space represents a line. 
   During the transformation, for each edge point in an input image: the values of d and α are calculated, and the bin of the Hough space, whose range includes the value of d and α for each edge point, is incremented. Once all the edge points in the input image have been examined, the Hough space is searched for maximum values, using peak detection, a method known in the art. The bin having the highest value in the Hough space represents the strongest line detected in the input image, the second highest local maxima represents the second strongest line detected, and so forth. 
   Each bin  402  in the Hough space represents a discrete range of angles and a discrete range of distance vectors.  FIG. 5  shows an instance of a quantization of the angles for a Hough space, where 360° is divided into  64  bins. Each of the  64  bins has a range of 5.62 degrees per bin, where the first bin accommodates the angles within 0-5.62°, the second bin accommodates the angles within 5.62°-11.24°, and so on. 
   Typically, the line-angle range and/or distance-vector range for each bin in the Hough space, and the divisions of ranges between the bins, are driven by system and application parameters, and often do not exactly represent the line angles or distance vectors in a given. image. Thus, the partitioning of the line angle and: the distance vector into discrete bins hinders detecting lines whose edge points straddle the boundaries, such as lines with a line angle of 5.62°, in the above example. The edge points of such lines, typically, transform into more than one bin, thus, it is more difficult to detect these lines, as is further discussed in J. Brian Burns, Allen R. Hanson, and Edward M. Riseman, “Extracting Straight Lines”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(4), 1986. 
   The effects of dispersion and the number of partitions in an axis are decreased by increasing the range of data accepted in each bin. However, increasing the range decreases precision of the line angles and/or distance vectors. As illustrated using  FIG. 6 , which depicts a 59° line  600  and a 51° line  610  and their respective discrete-angle histograms  602  and  612  derived from a Hough space. A Hough space created using a four-bit representation for angle partitions the line-angle axis of the Hough space so that the edge points  604  and  614  of both lines  600  and  610  all map to bin two in the Hough space. Thus, the ability is lost to distinguish between a 51° line and 59° line in Hough space. 
   Other techniques known in the art, such as a Point Spread Function update method, for example, also decrease dispersion effects. For each edge point, the Point Spread Function update method increments more than one bin with a partial weighting. Although the edge points do not contribute 100% to the weight of the appropriate bin, it is less likely any edge points fail completely to contribute to the weight of the appropriate bin. Although the Point Spread Function update method compensates, in part, for dispersion, it also causes a loss of precision because the Point Spread Function tends to smear the Hough space peaks. 
   An additional problem with image processing smaller contours is the inability to identify appropriate groupings of edge points of each contour given the superfluous noise and background clutter. The paper W. Eric L. Grimson and Daniel P. Huttenlocher “On the Sensitivity of the Hough Transform for Object Recognition,” Transactions on Pattern Analysis and Machine Intelligence, 12(3), 1990, discusses how line finding and object detection using Hough transforms suffers from superfluous noise and background clutter, particularly when trying to detect shorter lines. 
   Also, the Hough transform is only as precise as the underlying edge-point data, which is limited according to current technology. Further, the precision cannot be greatly increased by interpolating the edge-point data to a higher number of bits because, eventually, the interpolated bits do not represent meaningful precision. 
   SUMMARY 
   The invention provides methods and apparatuses for refining groupings of edge points that represent contours in an image. A contour is refined by refining the edge points of which the contour is comprised. More particularly, the grouping of edge points representing a contour is changed by annexing an edge point (termed annexed edge-point) from a grouping to the contour grouping (termed a seed population) to create a refined grouping of edge points (i.e., a refined contour). 
   Initially, each of the groupings has a parameter range, and each edge point within the groupings has a parameter substantially within the respective parameter range. The parameter range of the seed population is termed a seed-parameter range. 
   Before the edge point can be annexed, a refined parameter for the edge point is calculated. An edge point is annexed by the seed population when the refined parameter of the edge point is substantially within the seed-parameter range. Thus, the edge points of the refined grouping (i.e., the seed population plus the annexed edge points) all have a parameter, or a refined parameter, within the same range as the parameter of the seed population (i.e., the seed-parameter range). 
   The refined parameter is generated by re-calculating the parameter of the annexed edge-point. In one embodiment, the refined-parameter calculation differs from the parameter calculation for each edge point in that the refined-parameter calculation uses the individual characteristics of the entire seed population, while the parameter calculation uses individual characteristics of the edge point. More particularly, an intermediate characteristic is calculated from the individual characteristics of the seed population, and the intermediate characteristic is used in the parameter calculation to generate the refined parameter. 
   In a preferred embodiment, the refined parameter for a Hough representation of a line is a refined distance-vector, and at least one of the parameters is a distance vector. The distance-vector calculation for each edge point is a function of the edge-point direction and edge-point position (i.e. the individual characteristics of the edge-point), while the refined-distance-vector calculation for the same edge point is a function, not only of the edge-point position (i.e. an individual characteristic), but also of the positions of the edge points from the entire seed population. 
   More particularly, the refined distance vector is calculated using an angle of a least-squares-fit line to the edge points of the seed population in the distance-vector calculation of a Hough line-transformation. A least-squares line is fit to the edge-point positions of the edge points in a local maxima bin, termed seed population, of the Hough space. The angle of the least-squares line, denoted an intermediate line-angle, is used to re-compute the distance vector of edge points in the bins that-neighbor the seed-edge population. The arguments of the refined-distance-vector equation are the intermediate line-angle and the edge-point position, which was computed during edge detection. If the refined distance-vector falls within the range of the seed-edge population, then the seed-edge population annexes the edge point, thus, becoming an annexed edge-point. In one embodiment, the annexed edge-point is removed from its original bin and added to the bin of the seed population. 
   In the preferred embodiment, the positions of the edge points in each grouping are stored. 
   Among others, the invention recognizes that retaining the position of edge points in a parameter space makes the positions available for other calculations, such as computing the line angle of each bin in the parameter space. Further, using the teachings herein, those skilled in the art should recognize that retaining edge characteristics throughout a transformation is advantageous in many applications. 
   In other embodiments, one or more edge points are annexed from the same and/or other groupings of edge points to one or more seed populations to further refine, and/or generate more refined groupings of edge points. 
   The contour to be refined is first chosen by ranking the groupings into an ordered set, where at least one of the groupings is denoted the seed population (i.e. the contour grouping to be refined). 
   In further aspects, groupings of edge points are denoted seed populations according to an order of the groupings of edge points in the ordered set. In one embodiment, groupings of edge points are ordered according to the value of variances among the collinear distances of the edge points in each of the bins and/or the number of the edge points in each of the bins. When more than one seed population is refined, the order in which the seed populations are refined is sequential, according to the position of the seed populations in the ordered set. 
   In further aspects, the invention scores the refined lines according to an edge-point polarization of each line. 
   In one embodiment, a dual hybrid space is created from a first parameter space and a second parameter space to refine one of the parameters of the contours. The first parameter space and the second parameter space contain the same edge points (i.e. data), and are offset from each other in a first dimension, such as angle or distance. The first parameter space and the second parameter space are merged to create the hybrid-space, where each of the edge points is represented once in the hybrid-space. Thus, the hybrid space allows refinement of the parameter represented on the first dimension. 
   In a preferred embodiment, edge points are annexed along one dimension of a Hough space, while a dual Hough space compensates for the second dimension by offsetting the two constituent spaces in the second dimension. Thus, both dimensions of the Hough space are refined. 
   The invention also recognizes that groupings of edge points can be refined by using characteristics of, the groupings, and/or the edge points in the groupings, in a way other than the way the grouping was generated. More particularly, using characteristics of, a primary grouping, and/or the edge points in the primary grouping, to compare an edge point of another grouping to the primary grouping, where the primary grouping is also called herein the seed population. 
   Among other advantages, the method recovers edge points, which are otherwise lost due to dispersion and/or quantization, by annexing the edge points into a primary grouping. The annexation of the edge points reinforces the primary grouping, while simultaneously reducing, and sometimes eliminating, the effects of dispersion. 
   Another advantage of the invention, as applied to line detection, is that the invention generates a line angle that is not limited to the precision of a single edge point. Instead, the line angle is interpolated based upon the position of all the edge points of the line. 
   The invention overcomes various problems with the prior art, including, but not limited to, minimizing the effect of, and decreasing the extent of, dispersion of edge points; minimizing the effect of the dispersion of edge points while maintaining accuracy of the grouping of edge points (i.e., keeping line angles accurate without making the bin ranges larger or without using the partial weighting method, for example); de-emphasizing the effect of quantizing ranges of features of edge points or quantizing ranges of parameters derived from features of edge points; finding a line that straddle boundaries between the edge-point quantizations in a Hough space; and decreasing the sensitivity of a Hough transform to false edge-point peaks due to noise or other superfluous edge points. 
   The invention is particularly helpful for accurately and robustly detecting straight-line contours in noisy, cluttered imagery. 

   
     In further aspects, the invention provides apparatuses in accord with the methods described above. The aforementioned and other aspects of the invention are evident in the drawings and in the description that follows. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will be more fully understood from the following detailed description, in conjunction with the accompanying FIGS., wherein: 
       FIG. 1  depicts a contour, edge-points of the contour, and edge-point directions. Also shown is a histogram of the edge-point directions; 
       FIG. 2  is a graphical representation of an edge and the direction of an edge point; 
       FIG. 3  illustrates a line-parameterization format that includes a distance vector, line angle for a line, and a collinear distance of one of the edge points of the line; 
       FIG. 4A  is a graphical diagram of a traditional Hough space for lines, which uses the line format depicted in  FIG. 3 ; 
       FIG. 4B  is a graphical diagram of an annotated Hough space, which uses the line format depicted in FIG.  3 . Also shown is a bin thereon, and an edge-point array; 
       FIG. 5  depicts an instance of a partitioning scheme of a continuous-angle range into discrete, quantized values; 
       FIG. 6  depicts instances of two contours, edge-points of the contour, edge-point directions, and their respective angle histograms; 
       FIG. 7  is a schematic diagram of a machine-vision system for practice of the invention; 
       FIG. 8  is a flowchart summarizing operation of a preferred embodiment of a method according to the invention that refines a contour represented on a parameter space; 
       FIG. 9  is a flowchart detailing operation of annexing for one embodiment of the method of  FIG. 8 ; 
       FIG. 10  is a diagram illustrating the recovery of edge points using the annexing of  FIG. 9 ; 
     FIG.  11  and  FIG. 11A  are diagrams illustrating two possible groupings of the same edge points; 
       FIG. 12  is a diagram illustrating a plurality of lines, including an idealized line, a line exhibiting an accumulated-line-fit error, a line with edge-point-polarization errors, a line having a small edge-point density, a line having both an accumulated-line-fit error and edge-point-polarization error, and a line having an accumulated-line-fit error, edge-point-polarization error, and small edge-point density, respectively; and 
       FIG. 13  is a flowchart detailing operation of an embodiment of a method according to the invention that creates a hybrid-parameter space. 
   

   DETAILED DESCRIPTION 
   The methods and apparatuses disclosed herein refine groupings of edge points that represent contours in an image. The method is particularly useful for refining straight-line segments identified using a Hough transformation, where the straight-line segments are from production images typically available in the semiconductor and electronics industries. Though this is the form of a preferred embodiment, this embodiment should be considered illustrative, and not restrictive. 
     FIG. 7  illustrates a machine system  710  of the type in which the invention is practiced. The system  710  includes a capturing device  716 , such as a conventional video camera or scanner that generates an image of an object  712 . Image data (or pixels) generated by the capturing device  716  represent, in the conventional manner, the image intensity (e.g. color or brightness) of each point in the scene at the resolution of the capturing device  716 . 
   The capturing device  716  transmits the digital image data via a communications path  718  to an image analysis system  720 . This can be a conventional digital data processor, or a vision processing system of the type commercially available, for example, from the assignee hereof, Cognex Corporation, programmed in accord with the teachings hereof to refine groupings of edge points from an image. 
   The image analysis system  720  may have one or more central processing units  722 , main memory  724 , an input-output system  726 , and one or more disk drives (or other mass storage device)  728 , all of the conventional type. 
   The system  720  and, more particularly, central processing unit  722 , is configured by programming instructions according to the teaching hereof to refine groupings of edge points from an image, as described in further detail below. Those skilled in the art will appreciate that, in addition to implementation on a programmable digital data processor, the methods and apparatuses taught herein can be implemented in special purpose hardware. 
     FIG. 8  illustrates a flowchart detailing a preferred embodiment of the method of the invention, where steps of the method are denoted in the detailed description in parentheses. One instance of a preferred embodiment is refining contours that are represented on a parameter space. 
   First, an input image is acquired ( 800 ), and, optionally, pre-processed ( 802 ), as known in the art. The pre-processing is application specific, and can include known techniques, such as smoothing and sub-sampling, for example. 
   Next, the edge data is generated ( 804 ) using edge detection, a technique known in the art, such as Sobel edge detection, for example. The edge data generated includes, edge-point position, edge-point direction, and edge-point magnitude. In a preferred embodiment, the edge-point position is generated to sub-pixel precision by the method described in commonly assigned U.S. Pat. No. 5,657,403 or other tools known in the art. 
   Although edge data is generated for many positions in the image, the edge data is significant only for edge points having stronger edge-point magnitudes. Insignificant edge points due to frame grabber noise, other imaging environment issues, or random fluctuations in pixel values, typically, increase processing time without adding precision, and often make it difficult to evaluate the edge data in the image. Optionally, these insignificant edge points are removed. In addition, edge-point magnitude values usually increase gradually in a “smear” as they approach an edge and then decrease as the edge is crossed. Optionally, some of the edge points that are near, but not at, an edge are also removed. 
   Preferably, the edge points are removed using peak detection ( 806 ), a technique known in the art, which thins out the edge points before the edge points are used to generate the parameter space ( 808 ). Optimally, the peak detector removes the edge points that are not peak points, thereby, leaving a single point-wide contour. As known in the art, peak points, typically, are stronger than an ambient level and have a value that is greater than, or equal to, the neighboring points of a two-point, four-point, or eight-point neighborhood, as further described in Cognex 3000/4000/5000, Programmable Vision Engines, Image Processing, Chapter 4 Edge Detection Tool, pages 215-216, (1996) incorporated herein by reference. 
   Next, a parameter space is formatted to store the edge-point data. The parameter space used depends on the contour being refined and the parameterization chosen for the contour, where the contour can be a line, a circle, an arc, or a generic boundary, for example. Preferably, the contour is one that can be defined by a mathematical description. Further, as known in the art, the same contour can be represented by multiple parameterizations. It should also be apparent that one or more parameters can be represented for each contour on the parameter space. 
   In a preferred embodiment, the contour refined is a line, parameterized by d  304  and α 302 , illustrated on  FIG. 3 , and represented on a Hough space. The size of the Hough space along the angle axis is computed using principles known in the art, and as further described in Cognex 3000/4000/5000, Programmable Vision Engines, Vision Tools, Chapter 3 Line Finder, pages 166-175, (1996) incorporated herein by reference.  FIG. 4B  depicts an instance of an annotated Hough space. The size of the Hough space along the distance-vector axis  402 , denoted L space , is a function of the maximum edge-point position and the resolution chosen by the user, which can be computed using the following equation: 
               L   space     =       ⌈           l   2     +     h   2         g     ⌉     +   1             [   4   ]             
 
Where g is the range of d for each bin, also called herein the granularity, (typically set from 0.5 to 2.0), and l, h, are the width and height, respectively of the input image. Other techniques can also be used to compute the Hough-space dimensions without departing from the scope of the invention.
 
   In a preferred embodiment, the parameter space does not just contain the weight of the edge points in each of the bins; the parameter space is annotated to also contain references to edge-point data. In the annotated Hough space example of  FIG. 4B , each Hough bin  408  will contain a weight field  410  and an edge-point list  412 , which contains the addresses of the edge points contributing to the bin. The edge-point list  412  is represented mathematically as a one-dimensional array, denoted EPL d,α  (EP 0  . . . EP n ), containing the addresses of each edge-point array  414 , such as address EPL(EP 0 ). The sum of all edge points in the edge-point lists  412  of all the bins  408  must equal the number of edge points input into the Hough transform, denoted here as N. 
   An edge-point array  414 , associated with each address of the edge-point list  412 , contains edge-point data  416 , generated earlier during the edge-detection step ( 804 ) and, optionally, the peak detection step ( 806 ) of  FIG. 8 , and data generated from the Hough processing  418 . The edge-point data  416  includes (X, Y), M and/or θ, where which edge-point data is required will depend upon how the edge-points are annexed and other optional steps, as hereinafter described. The Hough-processing data includes the Hough bin address (“HBA”)  420  to which the edge point belongs, and optionally d, α, and c. 
   In a preferred embodiment, the edge-point list  412  is generated and the HBAs  420  initialized using a two pass technique. The first pass increments the weight  410 , W, of each bin  408  pursuant to the Hough transform algorithm previously described, and also initializes the Hough bin address  420 , HBA, for each edge-point array  414 , EP n . The second pass sets the length of each edge-point list, n, as the value of the weight  410 , W, of each of the bins  408 ; and fills the edge-point list  412 , EPL, by adding the address of each edge-point array  414  to the edge-point list  412 , EPL, after examining the HBA  420  associated with each edge-point array  414 . As necessary, for each embodiment, the other Hough-transform data, being d, α, and c is added to the edge-point array  414 , during the first pass, when the HBA is initialized. Thus, each edge-point array  414  is assigned a Hough bin  408 , equal to the HBA, and each non-zero weighted Hough bin  408  will contain an address list of the edge points contributing to the respective Hough bin, that is the EPL d,α . 
   Returning to  FIG. 8 , next, the weight of the bins of the parameter space is searched, in at least one dimension, for local maxima, using peak detection previously described ( 810 ). If the groupings are represented as a multi-dimensional array, peak detection is employed in one or more dimensions. Preferably, when one-dimensional peak detection is employed on a multi-dimensional array, the dimension chosen for peak detection is the dimension that exhibits more dispersion of the data or alternatively, it is the dimension for which an embodiment of the hybrid-space of  FIG. 13  cannot partially compensate. 
   The local maxima found are termed seed-peaks, and the seed peaks are ranked according to their weight ( 811 ). Other ranking schemes that are tailored to an application can be used without departing from the scope of the invention. 
   The seed peaks are primary peaks, and, therefore, more likely to represent the proper parameterization of the contour (e.g. d and α of lines from the image in the Hough space example). Considerations, such as processing time, can lead to denoting only a sub-set of the local maxima as seed peaks, without departing from the scope of the invention. 
   In one embodiment, the seed peaks are ranked according to a spatial distribution of the edge points of the peak in addition to weight of the peak. For lines, the spatial distribution is measured as the variance of the collinear distances of the edge points of the peak. A preferred embodiment ranks lines having more spatially distributed edge points higher than more dense lines, when both lines have substantially the same weight. The invention recognizes that a subsequent line fit, as described hereinafter, is more accurate on edge points distributed over a greater spatial range. Using the teachings herein, those skilled in the art should recognize that the spatial distribution of lines could be used alone, or in conjunction with, other parameters, such as weight, to determine the quality of a line. 
   Further, using the teachings herein, those skilled in the art should recognize that the spatial distribution of other contours or groupings could be used to bias the designation of a grouping as a primary grouping. 
   Next, one or more of the edge points are annexed, from one or more bins, to one or more seed peaks ( 812 ), thereby, refining the groupings of edge points in one or more bins, as is further described with reference to FIG.  9 . 
     FIG. 9  details the annexation operation of one embodiment of the method of  FIG. 8 , where steps of the operation are shown in the detailed description in parentheses. The ranking of the seed peaks is input ( 900 ) into the annexation operation. 
   Preferably, each seed peak is examined sequentially according to the position assigned during ranking ( 902 ). Consequently, the edge points of a seed peak can be annexed to a higher ranking seed peak before the seed peak is examined. Other heuristics can be used without departing from the scope of the invention. 
   Using one embodiment of the Hough space example, an edge point is annexed to a seed peak ( 908 ) by re-calculating the distance vector of the edge point ( 906 ), using a new edge-point direction, denoted θ intermediate , derived from a least-squares-fit line to the edge points of the seed-peaks ( 904 ) in the distance-vector calculation of a Hough transformation, instead of using the edge-point direction, θ, which was previously determined during edge detection ( 804 ). This example is described using the diagram of  FIG. 10 , which illustrates the recovery of edge points, not drawn to scale, with continuing reference to FIG.  9 . 
     FIG. 10  illustrates fourteen edge points and corresponding edge-point directions hypothetically generated using the Hough transform equations hereinbefore described. Six edge points, denoted with a circle, share a common edge-point direction and are the edge points of the seed peak in this example, denoted the seed population  1000 . Two sets of four other edge points denoted by triangular edge points  1006  and square edge points  1008 , respectively, represent two other adjacent bins of edge points along the distance-vector axis, denoted a triangle bin and a square bin, respectively. 
   The new edge-point direction, denoted θ intermediate , is generated by first fitting a least-squares line  1002  to the positions of the seed population  1000  ( 904 ). The angle  1004  α intermediate  of the least-squares line  1002  is converted into an edge-point direction θ intermediate , using the following equation:
 
θ intermediate(degrees) =α intermediate −90°  [5]
 
   Next, in a preferred embodiment, a parameter of the edge points of at least one adjacent bin is recomputed. In this example, the triangle bin along the distance-vector axis is accessed, and the distance vector of the triangular edge points  1006  is re-calculated using θ intermediate  and the underlying triangular edge-point positions in the distance-vector calculation, represented mathematically as follows:
 
 d   refined   =x ·sin(θ intermediate ) −y ·cos(θ intermediate )  [6]
 
   Next, if d refined  of any of the triangular edge points  1006  are within the range of d for the seed population  1000 , then the triangular edge points  1006  are annexed to the seed population  1000  ( 908 ). 
   After all the edge points in the triangular bin are examined, a termination condition is examined ( 910 ), which determines whether another bin will be examined. Numerous termination conditions can be used without departing from the scope of the invention, such as a condition which balances processing time over precision, for instance. In a preferred embodiment, the termination condition is that a new bin is not accessed after either finding an empty bin (i.e. a bin having a null weight) or no edge points are annexed from a non-empty bin along both directions of the parameter axis (e.g. both directions of the distance-vector axis). 
   In this example, after the triangular edge points  1006  are annexed to the seed population  1000 , the termination condition is not met ( 910 ) so the square bin is accessed ( 906 ). d refined  is computed for each of the square edge points  1008  ( 906 ), and the square edge points  1008  are annexed to the seed population  1000  ( 908 ). When all the square edge points  1008  have been examined, the seed population  1000  is refined (i.e. augmented) from a weight of six to a weight of fourteen, including six circular edge points  1000 , plus four triangular edge points  1006 , and four square edge points  1008 . 
   Once annexing for one seed population is complete (e.g. the termination condition ( 910 ) is met), the next seed peak is selected ( 902 ), for which the steps ( 904 )-( 910 ) are repeated until no more seed peaks remain to be selected ( 912 ). 
   Other fitting techniques can be used to fit a contour without departing from the scope of the invention, such as an ellipse fit, for example. 
   Instead of calculating θ intermediate , d intermediate  could be calculated using the edge points of the seed-peaks, by averaging, for example. Thereafter α refined  is calculated instead of d refined  for the edge points of the other bins, and compared with the seed-peak range for α refined . 
   Additionally, c refined  can be calculated and used alone, or in conjunction with, the d refined  or α refined  to determine if the edge point should be annexed to the seed population. 
   Further, it should be apparent that the distance vector does not need to be re-calculated for all the edge points in each bin, and other variations, depending upon the image and application, can be used, such as, only recalculating d for every third edge point in each bin. 
   Similarly, not every bin needs to be accessed. Accessing just the neighboring bins or every third bin, for example, may be sufficient for certain applications. In applications other than Hough, the accessed bins are chosen according to their relative position along a boundary or their relative position as stored in a histogram, for example. 
   Turning to  FIG. 11 , with continuing reference to  FIG. 8 ,  FIG. 11  illustrates an instance of four refined seed populations of edge points  1100 ,  1102 ,  1104 , and  1106  (i.e. lines) that were generated by the peak annexation ( 812 ). 
   Next, optionally, a second fitting algorithm is performed for each refined seed population to which edge points were annexed ( 814 ). For example, four line fits are performed to the edge-points  1114  of each of the seed populations  1100 ,  1102 ,  1104 , and  1106 , respectively. A bisector (not shown) of each pair of parallel lines  1118  represents the line generated from the least-squares line fit to each of the refined seed populations  1100 ,  1102 ,  1104 , and  1106 . 
   Some applications may require reporting closely spaced contours, such as lines  1100 ,  1102 ,  1104 , and  1106  as one or two contours, depending upon the objectives of the application ( 816 ). For example, in a wirebonder application, one line segment should be reported for each side of a lead. A more abstract definition of a line than that employed heretofore is used to merge the lines  1100 ,  1102 ,  1104 , and  1106  or other contours. The merging is accomplished using well documented techniques, such as techniques of data clustering analysis, see Anil K. Jain and Richard C. Dubes, “Algorithms for Clustering Data” Chapter 3, pp. 89-101, Prentice Hall, Englewood Cliffs N.J. 1988 incorporated herein by reference. 
   In one embodiment, lines are grouped ( 816 ) by merging all lines having distance-vector values and angle values within a user-supplied tolerance of the distance value and angle value of the refined seed peak with the highest population. Which in this example, is a user-supplied delta from the distance vector and line angle values of the line  1100 . The merging results in two groups  1108  and  1110 , shown in  FIG. 11A , instead of four  1100 ,  1102 ,  1104 , and  1106 . 
   It should be apparent, that other higher level grouping criteria can be used without departing from the scope of the invention. 
   If the contours were optionally merged ( 816 ), another iteration of the fitting algorithm is performed on the merged segment ( 818 ). A bisector (not shown) of each pair of parallel lines  1118  represents a line generated from a least-squares line fit to each of the merged lines  1108  and  1110 . 
   Next, the lines are optionally scored ( 820 ) and passed to another algorithm or reported to a user ( 822 ). 
   In a preferred embodiment, the quality of a line is based upon. a composite score of three independent intrinsic properties: edge-point density, accumulated-line-fit error, and edge-point polarization. 
     FIG. 12  illustrates the three properties. Line  1200  represents an idealized line that has no accumulated-line-fit error (i.e., each edge-point position coincides substantially exactly with the line fit through it); has unit edge-point density (i.e., the edge-points are substantially equally spaced); and has an ideal edge-point polarization (i.e., all the edge-point directions are substantially identical and orthogonal to the line angle.) Line  1202  has an accumulated-line-fit error, where one definition of the error is the orthogonal distance from each edge point to the line summed for all the edge-points of the line. Line  1204  has an edge-point-polarization error, where the error is characterized as the standard deviation of the edge-point directions plus the difference between the mean of the edge-point directions and the expected direction (i.e., the line angle−90°). Other definitions of edge-point polarization error can be used without departing from the scope of the invention, such as using only standard deviation, for example. Line  1206  has unequally spaced edge points, and thus, has an edge-point density less than one. Line  1208  has both accumulated-line-fit and edge-point-polarization errors. Line  1210  has a combination of all three errors. 
   Edge-point density and accumulated-line-fit error are documented in the art as measures of line quality, see, Bertold K. P. Horn, Robot Vision, pp. 47-55. MIT Press, Cambridge Mass., 1993, incorporated herein by reference. 
   The invention recognizes that edge-point polarization provides further information about the quality of a line, and is useful alone, or in conjunction with, edge-point density, accumulated-line-fit error, or other line characteristics. Edge-point polarization of a line, and the use of it as a measure of quality of a line, is a recognition of the invention. 
   An alternate embodiment further refines the extraction of contours by employing a hybrid-parameter space, which is described with reference to FIG.  13 . Two parameters spaces are created ( 1300 - 1302 ) and ( 1304 - 1306 ), space A and space B, respectively, each having bin divisions offset from the other by one-half of a bin; and then merged into one hybrid-space ( 1310 ) so that each of the edge points is represented once in the hybrid-space. For example, at an angle quantization of five bits (32 states), which yields a resolution of 11.25 degrees/bin, an initial Hough bin using Map A covers the range from 0 to 11.25°, while in the initial Hough bin in Map B covers the range 354.37 to 5.65°. The edge points are represented once on the A space and once on the B space. 
   The invention recognizes that initially, lines that straddle the boundaries in one mapping are centered within a bin in the second mapping, thus, the edge points will cluster more in an alternate mapping. 
   Next, the edge points are merged ( 1310 ) into one hybrid-space such that each of the edge points is represented once in the hybrid-space. Which mapping, map A or map B, of the edge point is retained in the hybrid-space is determined using a voting procedure, and the resultant hybrid-space is a hybrid space that is composed of bins from both mappings. 
   In one embodiment, the voting procedure to choose the bins for the hybrid-space is implemented using a two-pass technique adapted from the voting procedure described in J. Brian Burns, Allen R. Hanson, and Edward M. Riseman, “Extracting Straight Lines”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(4), 1986, incorporated herein by reference. In the first pass, each edge point votes for the bin of space A or space B that possesses the greater weight. At the end of the first pass, each bin in both spaces has a support count. In pass two, the bins for which more than 50% of their constituent edge points have supported them are propagated forward into the hybrid-space. Other voting procedures can be used without departing from the scope of the invention, such as biasing one space over the other, for example. 
   Additionally, the quantization of parameters from any parameter space, such as the distance-vector, for example, can be addressed by processing the parameters as described with reference to  FIG. 13 , without departing from the scope of the invention. 
   Further, it should be apparent to one skilled in the art that more than two parameter spaces can be merged to create the hybrid-space without departing from the scope of the invention, where the spaces are offset by a fraction of a bin. 
   It should also be apparent that the fractional offset can divide the bin equally, such as ½ and ½, or unequally, such as ¾ and ¼, and will depend upon the application. 
   It should be apparent to one skilled in the art that the edge points can be grouped by other Hough transforms, such as Hough circles or Hough ellipses, for example. 
   Further, the edge points of a line can be grouped using other Hough parameterizations, such as a slope-intercept parameterization of a line, for example. 
   It should also be apparent that the invention can refine one or more parameters stored on a one-dimensional space or multi-dimensional space, respectively such as the parameterization of a Hough ellipse. 
   It should also be apparent that the group examined for annexing can be the adjacent group or other group directed by an application specific heuristic, which ends as directed by the termination condition, as previously described. 
   Preferably, the group characteristic is re-calculated using some aspect of the seed population, such as described with reference to  FIG. 9 , for example. The exact nature of the recalculation is application specific, and can be, for example, using a second boundary extracting method to refine edge data. 
   It should be apparent that the method can refine many different coarser groupings of edge points. However, the method easily lends itself to refining groupings of edge points in an image that are related to each other by at least one mathematical definition, such as by an equation or approximation. 
   Those skilled in the art will appreciate that some, or all, of the steps of preprocessing the image, detecting edge points, detecting peaks, annexing edge points, merging lines, scoring lines, and fitting lines described hereinbefore can be combined and effected as hardware implementations, software implementations or a combination thereof. 
   Furthermore, while many operations are described herein utilizing an image from a industry application, it should be appreciated that any of the images described herein can be subject to further processing, such as by filtering using a gaussian filter, median filter, smoothing filter, morphological filter or the like known in the art, in order to improve image quality. 
   Those skilled in the art will also realize that using reduced-resolution images to generate the edge points, for example, could decrease processing time. Further, the method can use any combination of full-resolution and reduced-resolution images. However, use of reduced-resolution images typically results in a loss of accuracy. 
   Those skilled in the art will realize that processing time can also be decreased by performing any of the computations described herein using sampled data, such as generating best-fit equations from sampled data, for example. Sampled data is a subset of the available data points, such as every third data point, for instance. 
   Other modifications and implementations will occur to those skilled in the art without departing from the spirit and the scope of the invention as claimed. Accordingly, the above description is not intended to limit the invention except as indicated in the following claims.