[...]... in Section 2.1 with global thresholding methods and continuing with adaptive methods in Section 2.2 W Burger and M.J Burge, Principles of Digital Image Processing: Advanced Methods, Undergraduate Topics in Computer Science, DOI 10.1007/97 8-1 -8 488 2-9 1 9-0 _2, © Springer-Verlag London 2013 5 6 2 Automatic Thresholding (a) (b) (c) (d) (e) (f) (g) (h) Figure 2.1 Test images used for subsequent thresholding... grayscale histogram to W Burger and M.J Burge, Principles of Digital Image Processing: Advanced Methods, Undergraduate Topics in Computer Science, DOI 10.1007/97 8-1 -8 488 2-9 1 9-0 _1, © Springer-Verlag London 2013 1 2 1 Introduction calculate a single threshold value to be applied uniformly to all image pixels The second part presents techniques that adapt the threshold to the local image data by adjusting... problem of creating a faithful black-and-white (i e., binary) representation of an image acquired under a broad range of illumination conditions This is closely related to histograms and point operations, as covered in Chapters 3–4 of Volume 1 [20], and is also an important prerequisite for working with region-segmented binary images, as discussed in Chapter 2 of Volume 2 [21] The first part of this... 1 Introduction This third volume in the authors’ Principles of Digital Image Processing series presents a thoughtful selection of advanced topics Unlike our first two volumes, this one delves deeply into a select set of advanced and largely independent topics Each of these topics is presented as a separate module which can be understood independently of the other topics, making this volume ideal for... a small set of data (256 values in case of an 8-bit histogram); they can be grouped into two main categories: shape-based and statistical methods Shape-based methods analyze the structure of the histogram’s distribution, for example, by trying to locate peaks, valleys, and other “shape” features Usually the histogram is first smoothed to eliminate narrow peaks and gaps While shape-based methods were... Features 229 7.1 Interest points at multiple scales 230 7.1.1 The Laplacian -of- Gaussian (LoG) filter 231 7.1.2 Gaussian scale space 237 Principles of Digital Image Processing • Advanced Methods xii 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.1.3 LoG/DoG scale space 240 7.1.4 Hierarchical scale... value for binarizing the image As the name implies, histogram-based methods calculate the threshold primarily from the information contained in the image s histogram, without inspecting the actual image pixels Other methods process individual pixels for finding the threshold and there are also hybrid methods that rely both on the histogram and the local image content Histogram-based techniques are usually... transform-based solutions that indeed afford invariant and unambiguous shape matching Chapter 7 gives an in-depth presentation of David Lowe’s Scale-Invariant Local Feature Transform (SIFT), used to localize and identify unique key points in sets of images in a scale and rotation-invariant fashion It has become an almost universal tool in the image processing community and is the original source of many... total image variance σI is the sum of the within-class variance and the between-class variance, 2 2 2 σI = σw (q) + σb (q) (2.24) 2 Since σI is constant for a given image, the threshold q can be found by ei2 ther minimizing the within-variance σw or maximizing the between-variance 2 2 σb The natural choice is to maximize σb , because it only relies on first-order statistics (i e., the within-class... fingerprint (b), ARToolkit marker (c), synthetic two-level Gaussian mixture image (d) Results of thresholding with the fixed threshold value q = 128 (e–h) 2.1 Global histogram-based thresholding Given a grayscale image I, the task is to find a single “optimal” threshold value for binarizing this image Applying a particular threshold q is equivalent to classifying each pixel as being either part of the background . Springer-Verlag 2013 1 OI 10.1007/97 8- - - - _1,Undergraduate Topics in Computer Science, D 1 84882 919 0 London W. Burger and M .J. Burge, Principles of Digital Image Processing: Advanced Methods, 2. international Principles of Digital Image Processing Advanced Methods Wilhelm Burger • Mark J. Burge With 129 figures, 6 tables and 46 algorithms © Springer-Verlag London 2013 Printed on acid-free. Interestpointsatmultiplescales 230 7.1.1 TheLaplacian -of- Gaussian(LoG)filter 231 7.1.2 Gaussianscalespace 237 xii Principles of Digital Image Processing • Advanced Methods 7.1.3 LoG/DoGscalespace 240 7.1.4