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Segmentation of Digital Images

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Mixed Raster Content

Part of the book series: Signals and Communication Technology ((SCT))

Abstract

Most of the world’s cultural and scientific heritage is still available in printed form. In the past decades a number of actions and projects targeted the digitization of the printed material and the disclosure of the wealth of this content through Web technologies. One of the obstacles in this distribution is the lack of an efficient method of managing the large volume of data involved in archives of scanned documents. Since, digital image segmentation is identified as of paramount importance in mixed raster content compression, this chapter introduces to the field of segmentation and provides a brief description of known segmentation techniques and their applications.

—We bring the interpretation process into awareness through tricks. First, we degrade the image, making interpretation difficult. Second, we provide competing organizations, making possible several conflicting interpretations of the same image. Third, we provide organization without meaning to see how past experience affects the process.

Peter Lindsay and Donald Norman

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Notes

  1. 1.

    The term ‘requires’ is used to denote the requirements relating to the HVS modeling.

  2. 2.

    Fisher linear discriminant (Brown 1999), is a clustering method, in which data of high dimensionality are projected on a line and a clustering is applied on the one dimensional space. The projection maximizes the distance between the average values of the classes, while, at the same time, it minimizes the variance within each class. The Fisher criterion that is being maximized for all line projections is defined for two classes as \(J(w)=\frac{|m_1-m_2|^2}{\sigma _1^2+\sigma _2^2}\), where m is the mean and \(\sigma ^2\) the variance of the classes.

  3. 3.

    Dynamic Programming is a method for problem solving, in which the solution path is designed in reverse (from the required outcome backwards to the beginning).

  4. 4.

    Region growing methods are bottom-up approaches, since they start by a single pixel and scale up to the overall image, whereas region splitting methods are top-down approaches, since they start by examining the whole image and scale down to the single pixel.

  5. 5.

    The term feature images denotes images that consist only of detected features and not typical pixel values.

  6. 6.

    In essence, Monte-Carlo statistics support the creation of a probability density function for the study of the effect of noise in the data. Monte-Carlo processes may prove useful in the study of the characteristics of a distribution, which are affected by noise, along with the study of characteristics that are crucial for the interpretation of the data.

  7. 7.

    This corresponds to a family of methodologies based on the analysis of repeated texture structures. In general, a number of matrices is calculated for a texture, and from those various other features are derived. The co-occurrence matrix is defined by a magnitude measure and an angle, and its mathematical expression is: \(C_{\theta ,d}(x,y)=|\{(m,n) \in (M \times N) \times (M \times N):d(m,n)=d, tan^{-1}(m-n)=\theta \mathrm {\;or\;} \pi - \theta \mathrm {\;and\;} f(m)=x, f(n)=y\}|\) where d(a,b) a distance measure, usually \(d[(a,b),(c,d)]=max(|a-c|,|b-d|)\) and \(f[(M \times N)\mapsto N(0,255)]\) the image under analysis. This definition guarantees that the matrix is diagonal.

  8. 8.

    Gabor expressed but not proved that the from all real-valued functions, the Hermite functions have the smallest product of implicit uncertainty. It holds that: \(g_n(x)=H_n(x)e^{-\frac{1}{2}x^2}\), with \(H_n(x)=(-1)^n e^{x^2} \frac{\mathrm {d}^n}{\mathrm {d}x^n} e^{-x^2}\) the Hermite polynomials.

  9. 9.

    MLP is the most common type of neural network. It is simple yet with powerful mathematical basis. The input data pass through layers of neurons, with the input layer consisting of as many neurons as the variables of the problem. The output layer has so many neurons as the desired output variables (often just one). The intermediate layers are called hidden.

  10. 10.

    Assuming S a closed subspace, then for any \(\epsilon >0\) and \(N(\epsilon )\) the minimum number of spheres of radius \(\le \epsilon \) necessary to cover all of S, if there exists a \({\delta }\) such that: \({\delta } = -\lim _{\epsilon \rightarrow 0^{+}} \frac{log N(\epsilon )}{log\epsilon }\), then \({\delta }\) is called the fractal dimension of S. In other words, the fractal dimension can be calculated by the limit of the ratio of the logarithm of change in the size of an object to the logarithm of the change in the measurement scale, as this scale tends to zero. In practice the following relation is used: \({\delta }=log(\mathrm {number\;of\;self-similar\;pieces})/log (\mathrm {magnification\;factor})\).

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    George Pavlidis

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Pavlidis, G. (2017). Segmentation of Digital Images. In: Mixed Raster Content. Signals and Communication Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-2830-4_3

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