Image Acquisitionand Proces

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Image Analysis 167 FIGURE 7.4 (a) High contract template. (b) Background variance. (c) Lighting variance. FIGURE 7.5 (a) Minimal template (b) Two instances found. (c) With background data. (d) One instance found. 7.1.2.1 Cross Correlation The mathematical process of image cross correlation is a simple one. Conceptually, the template is laid over the source image, and the intensity values for each corresponding pixel are individually multiplied, and then all of them are summed to produce a single correlation value. The template is then moved one pixel, and the process is repeated until the whole source image has been covered, and a matrix of correlation values has been created. The correlation value matrix is then scanned for its highest value; this position generally refers to the position in the source image that most closely matches the template. Of course, the correlation matrix can have several high values in it, corresponding to several instances of the template in the source image.
168 Image Acquisition Processing with LabVIEW To explain the concept of cross correlation further, consider a source image matrix of size a ¥ b, and a template image matrix of size c ¥ d (when c £ a and d £ b). If both the source image and template are normalized, the cross correlation matrix is populated using the following equation: b-1 a-1 = ij , ÂÂ ( )( ) xy , ( i+ x) ,( j+ y) x = 0 y= 0 CrossCorrelationMatrix Template Source If the images have not been normalized, then we must normalize them by dividing each element in the respective images by the square root of the sum of its squares: CrossCorrelationMatrix ij , = Ê Á Ë Â b-1 a-1 ÂÂ x = 0 y= 0 b-1 a-1 Â x = 0 y= 0 ( Templatexy , )( Source ( i+ x) ,( j+ y) ) ˆ Ê b-1 a-1 2 2 ˆ ( Templatexy , ) Source ˜ ÁÂÂ( xy , ) ˜ ¯ Ë x = 0 y= 0 ¯ Consider a cross correlation example with a 3 ¥ 3 template matrix (Table 7.1). To make the example simpler, let us assume that both the source S xy and template T xy images have been normalized. Performing the cross correlation between the images yields: TABLE 7.1 S 00 S 01 ... ... S 0b S 10 ... ... ... S 1b T 00 T 01 T 02 ... ... ... ... ... T 10 T 11 T 12 ... ... ... ... ... T 20 T 21 T 22 S a0 S a1 ... ... S ab Some values used in the cross correlation are undeÞned (i.e., those cells on the right and bottom of the matrix), and are consequently set to zero for calculations. This makes Þnding matches of a partial template near the edges unlikely. As you might imagine from the equation matrix shown previously, performing a cross correlation on large images can take some time, although increasing the size of the template will make the routine even slower. Also, if the rotation of the template is not known, the cross correlation will need to be repeated at a range of angles to achieve rotation-invariant matches. 7.1.2.2 Scale Invariant and Rotation Invariant Matching One of cross correlation’s biggest ßaws is its inability to match objects in a source image that are either a different size to the template, or have been rotated. If this
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IMAGE PROCESSING SERIES Series Edit
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Foreword The introduction of LabVIE
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FIGURE 1 Vision 6.1 FIGURE 2 Compan
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Acknowledgments My gratitude goes o
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Dedication To Don “old fella” P
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Contents Chapter 1 Image Types and
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Chapter 4 Displaying Images........
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Chapter 7 Image Analysis...........
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1 Image Types and File Management F
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Image Types and File Management 3 F
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Image Types and File Management 5 A
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Image Types and File Management 7 C
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Image Types and File Management 9 p
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Image Types and File Management 11
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Image Types and File Management 13
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2 Setting Up You should never under
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Setting Up 17 FIGURE 2.3 (a) Interl
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Setting Up 19 Linear Aray Light Sou
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Setting Up 21 FIGURE 2.7 National I
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Setting Up 23 2.1.3.2 Control and I
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Setting Up 25 FIGURE 2.11 X-Ray ima
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Setting Up 27 Apple Computer techno
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Setting Up 29 FIGURE 2.17 An inexpe
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Setting Up 31 Although this would b
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Setting Up 33 134 -115 \ Contrast =
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Setting Up 35 resolution printer wi
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Setting Up 37 C A B C Traditional T
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Setting Up 39 Camera Light Source O
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Setting Up 41 Camera Light Source (
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Setting Up 43 FIGURE 2.37 (a) An ob
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Setting Up 45 FIGURE 2.41 (a) PCB p
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48 Image Acquisition Processing wit
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8 Machine Vision A generally accept
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Machine Vision 219 TABLE 8.1 “IMA
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Machine Vision 221 TABLE 8.3 Input
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Machine Vision 223 packages, includ
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Machine Vision 225 good sense to ad
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Machine Vision 227 TABLE 8.4 “IMA
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Glossary 1-Bit Image An image compr
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Glossary 231 binary display device
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Glossary 233 spatial Þlters, each
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Glossary 235 Resolution There are t
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