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数字图像处理核心算法原理详解
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"《数字图像处理核心算法原理》是一本专为计算机科学本科学生设计的深入学习教材,它隶属于Undergraduate Topics in Computer Science (UTiCS)系列,该系列旨在为计算机与信息科学领域的学生提供高质量的教学资料。作者Wilhelm Burger和Mark J. Burger是他们在数字图像处理领域的知名专家,他们共同撰写了这本书。 本书强调了基础理论和现代方法的结合,以一种清晰、简洁的方式阐述了数字图像处理的核心算法。读者不仅可以借此书系统学习,也能作为自我学习或一学期课程的理想资源。书中包含大量的实例和问题,许多还提供了详尽的解题步骤,便于理解和实践。 作者们通过严谨的国际顾问团队,如来自牛津大学的Samson Abramsky、伦敦帝国理工学院的Chris Hankin、美国康奈尔大学的Dexter Kozen以及剑桥大学的Andrew Pitts,进行了审阅,确保了内容的专业性和准确性。 《数字图像处理核心算法原理》共123页,适合那些对图像处理技术感兴趣的大学生,无论是在理论层面上寻求深度理解,还是在实践中寻求技术应用的支持。此外,两位作者分别来自奥地利的诺布尔斯应用科学大学,他们的电子邮件地址供读者交流和获取更多资源。 这本书不仅涵盖了图像处理的基本概念,而且深入探讨了关键的算法策略,是每个计算机视觉、图像分析或机器学习专业学生不可或缺的参考资料。通过阅读这本书,读者将能提升对数字图像处理技术的理解,并掌握处理实际问题所需的实用技能。"
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1.2 Image Analysis 3
1.2 Image Analysis
Although image analysis is not the central theme of this book, most methods
described here exhibit a certain “analytical flavor” that adds to the elemen-
tary “pixel crunching” techniques described in the preceding volume [14]. This
intersection becomes evident in tasks like segmenting image regions (Ch. 2),
detecting simple curves and corners (Chs. 3–4), or comparing images (Ch. 11)
at the pixel level. All these methods work directly on the pixel data in a bottom-
up way without recourse to any domain-specific or “semantic” knowledge. In
some sense, one could describe all these methods as “dumb and blind”, which
differentiates them from the approach pursued in pattern recognition and com-
puter vision. Although these two disciplines are firmly grounded in, and rely
heavily on, image processing, their ultimate goals are much loftier.
Pattern recognition is primarily a mathematical discipline and has been
responsible for techniques such as probabilistic modeling, clustering, decision
trees, or principal component analysis (PCA), which are used to discover pat-
terns in data and signals. Methods from pattern recognition have been ap-
plied extensively to problems arising in computer vision and image analysis.
A good example of their successful application is optical character recognition
(OCR), where robust, highly accurate turnkey solutions are available for recog-
nizing scanned text. Pattern recognition methods are truly universal and have
been successfully applied not only to images but also speech and audio sig-
nals, text documents, stock trades, and for finding trends in large databases,
where it is often called “data mining”. Dimensionality reduction, statistical,
and syntactical methods play important roles in pattern recognition (see, for
example, [21,55,72]).
Computer vision tackles the problem of engineering artificial visual sys-
tems capable of somehow comprehending and interpreting our real, three-
dimensional world. Popular topics in this field include scene understanding,
object recognition, motion interpretation (tracking), autonomous navigation,
and the robotic manipulation of objects in a scene. Since computer vision has
its roots in artificial intelligence (AI), many AI methods were originally de-
veloped to either tackle or represent a problem in computer vision (see, for
example, [19, Ch. 13]). The fields still have much in common today, espe-
cially in terms of adaptive methods and machine learning. Further literature
on computer vision includes [2,24,35, 65,69,73].
Ultimately, you will find image processing to be both intellectually challeng-
ing and professionally rewarding, as the field is ripe with problems that were
originally thought to be relatively simple to solve but have, to this day, refused
to give up their secrets. With the background and techniques presented in this
text, you will not only be able to develop complete image processing solutions
4 1. Introduction
but will also have the prerequisite knowledge to tackle unsolved problems and
the real possibility of expanding the horizons of science.
2
Regions in Binary Images
In binary images, a pixel can take on exactly one of two values. These values
are often thought of as representing the “foreground” and “background” in the
image, even though these concepts often are not applicable to natural scenes.
In this chapter we focus on connected regions in images and how to isolate and
describe such structures.
Let us assume that our task is to devise a procedure for finding the number
and type of objects contained in a figure like Fig. 2.1. As long as we continue
Figure 2.1 Binary image with nine objects. Each object corresponds to a connnected region
of related foreground pixels.
W. Burger, M.J. Burge, Principles of Digital Image Processing, Undergraduate Topics
in Computer Science, DOI 10.1007/978-1-84800-195-4_ Springer-Verlag London Limited, 2009
©
2,
6 2. Regions in Binary Images
to consider each pixel in isolation, we will not be able to determine how many
objects there are overall in the image, where they are located, and which pixels
belong to which objects. Therefore our first step is to find each object by
grouping together all the pixels that belong to it. In the simplest case, an
object is a group of touching foreground pixels; that is, a connected binary
region.
2.1 Finding Image Regions
In the search for binary regions, the most important tasks are to find out which
pixels belong to which regions, how many regions are in the image, and where
these regions are located. These steps usually take place as part of a process
called region labeling or region coloring. During this process, neighboring pixels
are pieced together in a stepwise manner to build regions in which all pixels
within that region are assigned a unique number (“label”) for identification.
In the following sections, we describe two variations on this idea. In the first
method, region marking through flood filling, a region is filled in all directions
starting from a single point or “seed” within the region. In the second method,
sequential region marking, the image is traversed from top to bottom, marking
regions as they are encountered. In Sec. 2.2.2, we describe a third method that
combines two useful processes, region labeling and contour finding, in a single
algorithm.
Independent of which of the methods above we use, we must first settle on
either the 4- or 8-connected definition of neighboring (see Vol. 1 [14, Fig. 7.5])
for determining when two pixels are “connected” to each other, since under
each definition we can end up with different results. In the following region-
marking algorithms, we use the following convention: the original binary image
I(u, v) contains the values 0 and 1 to mark the background and foreground,
respectively; any other value is used for numbering (labeling) the regions, i. e.,
the pixel values are
I(u, v)=
⎧
⎨
⎩
0 a background pixel
1 a foreground pixel
2, 3,... aregionlabel.
2.1.1 Region Labeling with Flood Filling
The underlying algorithm for region marking by flood filling is simple: search
for an unmarked foreground pixel and then fill (visit and mark) all the rest of the
neighboring pixels in its region (Alg. 2.1). This operation is called a “flood fill”
because it is as if a flood of water erupts at the start pixel and flows out across
a flat region. There are various methods for carrying out the fill operation that
2.1 Finding Image Regions 7
Algorithm 2.1 Region marking using flood filling (Part 1). The binary input image I uses
the value 0 for background pixels and 1 for foreground pixels. Unmarked foreground pixels
are searched for, and then the region to which they belong is filled. The actual FloodFill()
procedure is described in Alg. 2.2.
1: RegionLabeling(I)
I: binary image; I(u, v)=0: background, I(u, v)=1: foreground
The image I is labeled (destructively modified) and returned.
2: Let m ← 2 value of the next label to be assigned
3: for all image coordinates (u, v) do
4: if I(u, v)=1then
5: FloodFill(I,u,v,m) use any version from Alg. 2.2
6: m ← m +1.
7: return the labeled image I.
ultimately differ in how to select the coordinates of the next pixel to be visited
during the fill. We present three different ways of performing the Fl oodFill()
procedure: a recursive version, an iterative depth-first version,andaniterative
breadth-first version (see Alg. 2.2):
(A) Recursive Flood Filling: The recursive version (Alg. 2.2, lines 1–8)
does not make use of explicit data structures to keep track of the image
coordinates but uses the local variables that are implicitly allocated by
recursive procedure calls.
1
Within each region, a tree structure, rooted at
the starting point, is defined by the neighborhood relation between pixels.
The recursive step corresponds to a depth-first traversal [20] of this tree
and results in very short and elegant program code. Unfortunately, since
the maximum depth of the recursion—and thus the size of the required
stack memory—is proportional to the size of the region, stack memory is
quickly exhausted. Therefore this method is risky and really only practical
for very small images.
(B) Iterative Flood Filling (depth-first): Every recursive algorithm can
also be reformulated as an iterative algorithm (Alg. 2.2, lines 9–20) by
implementing and managing its own stacks. In this case, the stack records
the “open” (that is, the adjacent but not yet visited) elements. As in the
recursive version (A), the corresponding tree of pixels is traversed in depth-
first order. By making use of its own dedicated stack (which is created in
the much larger heap memory), the depth of the tree is no longer limited
1
In Java, and similar imperative programming languages such as C and C++, local
variables are automatically stored on the cal l stack at each procedure call and
restored from the stack when the procedure returns.
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