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barcode generator project in vb.net CONTOURS in Software
CHAPTER 6 CONTOURS GS1  12 Drawer In None Using Barcode drawer for Software Control to generate, create UPC Symbol image in Software applications. UCC  12 Scanner In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. for curve fitting that are useful when some of the edge points have been incorrectly linked into the contour These incorrectly assigned points are called outliers Generating UPC A In C# Using Barcode generation for Visual Studio .NET Control to generate, create UPCA image in .NET framework applications. Create UPC Symbol In VS .NET Using Barcode generator for ASP.NET Control to generate, create Universal Product Code version A image in ASP.NET applications. Total Regression
GS1  12 Creator In .NET Framework Using Barcode encoder for .NET Control to generate, create UPC A image in .NET applications. Printing GTIN  12 In VB.NET Using Barcode printer for .NET framework Control to generate, create UPCA image in .NET applications. Classical linear regression minimizes the difference between a data point and the model in only one dimension, the dimension of the dependent variable For example, a functional model of the form GTIN  12 Maker In None Using Barcode drawer for Software Control to generate, create UPCA image in Software applications. UCC  12 Generation In None Using Barcode encoder for Software Control to generate, create GS1 128 image in Software applications. (639) EAN13 Drawer In None Using Barcode encoder for Software Control to generate, create GTIN  13 image in Software applications. Paint ANSI/AIM Code 128 In None Using Barcode drawer for Software Control to generate, create Code 128 Code Set C image in Software applications. relating the dependent variable y to the independent variable x, with the p model parameters al through a p , assumes that there are no errors in the independent variable x In machine vision, errors in the x and y coordinates of location are equally likely and the curve model may be a vertical line, for instance, which cannot be represented in functional form In machine vision, lines and other curve models are fitted to edges using total regression, which minimizes the sum of the squares of the perpendicular distances of the data points from the regression model The advantage of this technique is that it compensates for errors in both the x and y directions Total regression has actually already been presented in 2 where it was used to derive the equations for determining the orientation of a blob, although the term total regression was not used at the time To avoid problems when the line is vertical, represent the equation for a line by using polar coordinates: DataMatrix Creator In None Using Barcode generation for Software Control to generate, create ECC200 image in Software applications. Barcode Encoder In None Using Barcode generation for Software Control to generate, create barcode image in Software applications. x cos () + y sin ()  p = O
I2/5 Drawer In None Using Barcode maker for Software Control to generate, create 2/5 Interleaved image in Software applications. Scan Code 128A In C#.NET Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications. (640) Encode Code39 In Java Using Barcode generator for BIRT Control to generate, create USS Code 39 image in Eclipse BIRT applications. UPC  13 Drawer In VB.NET Using Barcode generator for Visual Studio .NET Control to generate, create EAN 13 image in VS .NET applications. Minimize the sum of the squared perpendicular distances of points (Xi, Yi) from the line: (641) The solution to the total regression problem is Creating Barcode In Visual Basic .NET Using Barcode generation for .NET Control to generate, create bar code image in .NET framework applications. Bar Code Scanner In .NET Framework Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. = x cos () + Ysin () Generate EAN13 In Java Using Barcode creation for Eclipse BIRT Control to generate, create EAN / UCC  13 image in BIRT reports applications. UCC  12 Maker In Visual Studio .NET Using Barcode creation for VS .NET Control to generate, create UCC.EAN  128 image in Visual Studio .NET applications. (642) 68 CURVE APPROXIMATION
with
 LXi n i=l
(643) (644)  LYi' n i=l
The orientation of the total regression line is tan2e with
e, given by
(645) 2 LX~Y~
i=l n n
(646) (64 7) LX  LY
i=l i=l
I xi = Xi  X
Yi = Yi  y
(648) (649) Total regression uses a leastsquares error norm that is optimal if the errors are from a normal distribution, but is not suitable if there are outliers present in the data In the case of fitting a curve model to edge data, outliers would occur if the edge linking procedure incorporated one or more edges from other contours into the edge list for a contour Outliers can occur even if the edge linking procedure performs flawlessly For example, consider a list of edges from two adjacent sides of a rectangle The corner must be identified in order to segment the edges into the two sides before fitting a line to the edges If the corner point is not identified correctly, some edges may be assigned to the wrong side, and these edges are outliers In general, errors in classification introduce errors into the regression problem that are not normally distributed In such a case, the errors may be modeled by a mixture distribution that combines a Gaussian distribution for modeling the normal errors with a broadtailed distribution for modeling the outliers due to imperfect classification CHAPTER 6 CONTOURS
Estimating Corners
The best method for estimating corners is to use one of the methods for fitting a line to edge points and then compute the intersection of the lines This method compensates for the error introduced by edge detection operators that round off the corners and is more accurate than using a corner detector which only uses local information Given the implicit equations for two lines, alx a2 x
+ b1y + Cl
(650) (651) + b2y + C2
the location of the intersection is (652) (653) If a 1 b2  a2bl is close to zero, then the lines are nearly parallel and cannot be intersected A good method for detecting corners is to try to fit pairs of lines over successive sublists of 2n + m edge points along the contour The parameter n is the number of edge points required for an accurate line fit, and the parameter m is the number of edge points to skip between the sides of the corner The gap skips over the edge points in the rounded part of the corner A corner is detected by testing the magnitude of a 1b2  a2bl against a threshold

