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526 results in Image processing and machine vision

Page 7 of 27

  • 7 - Mathematical Morphology

  • from Part II - Preprocessing
  • Wesley E. Snyder, North Carolina State University, Hairong Qi, University of Tennessee
  • Book:
    Fundamentals of Computer Vision
    Published online:
    25 October 2017
    Print publication:
    28 September 2017, pp 119-146

  • Summary

    I think the universe is pure geometry – basically, a beautiful shape twisting around and dancing over space-time.

    – Antony Garrett Lisi

    Introduction

    In this chapter, a study of shape begins. Throughout the remainder of this book we will continue to look at shape in many different ways. Here, the topic is introduced at the pixel level, providing some simple, local operations that modify shapes, changing connectivity, and providing nonlinear ways to treat noise.

  • • (Section 7.2) Binary morphology changes the shape of binary objects. We define the two basic morphological operators, dilation and erosion, on the basis of which two other operators, opening and closing, can be derived. We also discuss some interesting properties of these morphological operators and their applications in noise removal and edge linking.

  • • (Section 7.3) We extend the discussion to grayscale morphology and define the dilation and erosion operations when the objects are not described in binary values. We progress from grayscale morphology using flat structuring elements to the use of grayscale structuring elements.

  • • (Section 7.4) As one of the most important applications of morphological operations, we discuss the distance transform (DT) and different ways to compute the DT.

    • Morphological operations may be considered as either the result of set operations, or the result of composition of functions. Both these approaches are described in this chapter, in order to provide the student with the insight to see similarities and suitability. We will find that set-theoretic ways of thinking about morphology are most appropriate for binary images, and functional notation is more convenient for grayscale images. In section 7.5, an application example of combining dilation, erosion, and distance transform for the purpose of edge linking is provided to illustrate the power of these operations.

    Binary Morphology

    In this section, we first introduce two basic morphological operators, dilation and erosion. We then define opening and closing, two operators that are developed based on dilation and erosion. We also discuss interesting properties of these operators and their applications in solving computer vision problems.

  • 8 - Segmentation

  • from Part III - Image Understanding
  • Wesley E. Snyder, North Carolina State University, Hairong Qi, University of Tennessee
  • Book:
    Fundamentals of Computer Vision
    Published online:
    25 October 2017
    Print publication:
    28 September 2017, pp 149-199

  • Summary

    The partition between the sage and the fool is more slender than the spider web.

    – Kahlil Gibran

    Introduction

    Segmentation is the process of separating objects from background. It is the foundation for all the subsequent processes like shape analysis and object recognition.

    A segmentation of a picture is a partitioning into connected regions, where each region is homogeneous in some sense and is identified by a unique label. For example, in Figure 8.2 (a “label image”), region 1 is identified as the background. Although region 4 is also background, it is labeled as a separate region, since it is not connected to region 1.

    The term “homogeneous” deserves some discussion. It could mean all the pixels are of the same brightness, but that criterion is too strong for most practical applications. It could mean that all pixels are close to some representative (mean) brightness. Stated more formally [8.56], a region is homogeneous if the brightness values are consistent with having been generated by a particular probability distribution. In the case of range imagery [8.31] where we (might) have an equation that describes the surface, we could say a region is homogeneous if it can be described by the combination of that equation and some probabilistic deformation. For example, if all the points in a region of a range image lie in the same plane except for deviations whose distance from the plane may be described by a particular Gaussian distribution, one could say this region is homogeneous.

    In this chapter, several ways to perform segmentation are discussed.We progress through problems and methods of increasing complexity:

  • • (Section 8.2) Threshold-based techniques are guaranteed to form closed regions because they simply assign all pixels above (or below, depending on the problem) a specified threshold to be in the same region. However, using a single threshold only allows regions to be classified as “foreground” and “background.”

  • • (Section 8.3) Brightness segmentation into two classes is the simplest case. It becomes more challenging when color images are considered and similarities of colors must be considered.

  • • (Section 8.4) Another level of complexity occurs when it is necessary to determine whether two apparently separate regions are really one region. That is, do they touch? For this, we need connected components.

  • C - The Image File System (IFS) Software

  • Wesley E. Snyder, North Carolina State University, Hairong Qi, University of Tennessee
  • Book:
    Fundamentals of Computer Vision
    Published online:
    25 October 2017
    Print publication:
    28 September 2017, pp 362-368

  • Summary

    The objective of quickly writing good imaging software can be accomplished by using the image access subroutines in IFS. IFS is a collection of subroutines and applications based on those subroutines that support the development of image processing software in C and C++.

    Advantages of IFS

    Advantages of IFS include

    bullIFS supports any data type including char, unsigned char, short, unsigned short, int, unsigned int, float, double, complex float, complex double, complex short, and structure.

  • • IFS supports any image size, and any number of dimensions. One may do signal processing by simply considering a signal as a one-dimensional image.

  • • IFS is available on most current computer systems, includingWindows on the PC, Linux on the PC, and OS-X on the Macintosh. Files written on one platform may be read on any of the other platforms. Conversion to the format native to the platform is done by the read routine, without user intervention.

  • • A large collection of functions are available, including two-dimensional Fourier transforms, filters, segmenters, etc.

    • The IFS Header Structure

    All IFS images include a header that contains various items of information about the image, such as the number of points in the image, the number of dimensions for the image, the data format, the units and scan direction of each dimension, and so on. Also associated with the image is the actual data for the image. The image header includes a pointer to the image data. The user manipulates an image by calling some function in the IFS library; one of the arguments to the function will be the address of the header. From the information in the header, the IFS library functions automatically determine where the data is and how to access it. In addition to accessing data in images, the IFS routines automatically take care of allocating space in memory to store data and headers. Everything is totally dynamic in operation; there are no fixed-dimension arrays. This relieves the user of the difficulties involved with accessing data in arrays, when the arrays are not of some fixed size.

  • 11 - Representing and Matching Scenes

  • from Part III - Image Understanding
  • Wesley E. Snyder, North Carolina State University, Hairong Qi, University of Tennessee
  • Book:
    Fundamentals of Computer Vision
    Published online:
    25 October 2017
    Print publication:
    28 September 2017, pp 267-300

  • Summary

    One of these things is not like the other.

    – Sesame Street

    Introduction

    In this chapter rather than matching regions that we did in Chapter 10, we consider issues associated with matching scenes.

    Matching at this level establishes an interpretation. That is, it puts two representations into correspondence:

  • • (Section 11.2) In this section, both representations may be of the same form. For example, correlation matches an observed image with a template, an approach called template matching. Eigenimages are also a representation for images that use the concepts of principal components to match images.

  • • (Section 11.3) When matching scenes, we don't really want to match every single pixel, but only do matching at points that are “interesting.” This requires a definition for interest points.

  • • (Sections 11.4, 11.5, and 11.6) Once the interest points are identified, these sections develop three methods, SIFT, SKS, and HoG, for describing the neighborhood of the interest points using descriptors and then matching those descriptors.

  • • (Section 11.7) If the scene is represented abstractly, by nodes in graphs, methods are provided for matching graphs.

  • • (Sections 11.8 and 11.9) In these sections, two other matching methods, including deformable templates, are described.

    • As we investigate matching scenes, or components of scenes, a new word is introduced, descriptor. This word denotes a representation for a local neighborhood in a scene, a neighborhood of perhaps 200 pixels, larger than the kernels we have thought about, but smaller than templates. The terms kernels, templates, and descriptors, while they do connote size to some extent, are really describing how this local representation is used, as the reader will see.

    Matching Iconic Representations

    Matching Templates to Scenes

    Recall that an iconic representation of an image is an image, e.g., a smaller image, an image that is not blurred, etc. In this section, we need to match two images.

    A template is a representation for an image (or sub-image) that is itself an image, but almost always smaller than the original. A template is typically moved around the target image until a location is found that maximizes some match function. The most obvious such function is the sum squared error, sometimes referred to as the sum-squared difference (SSD),

    which provides a measure of how well the template (T) matches the image (f) at point x, y, assuming the template is N × N.

  • 4 - Images: Representation and Creation

  • from Part I - Preliminaries
  • Wesley E. Snyder, North Carolina State University, Hairong Qi, University of Tennessee
  • Book:
    Fundamentals of Computer Vision
    Published online:
    25 October 2017
    Print publication:
    28 September 2017, pp 39-48

  • Summary

    Computers are useless. They can only give us answers.

    – Pablo Picasso

    Introduction

    Since you have already had a course in image processing, it should not be necessary to describe how images are formed. Representations, however, are another matter. This chapter discusses various image representation schemes as well as a way of treating images as surfaces.

  • • (Section 4.2) In this section, we discuss mathematical representations both for the information contained in an image and for the ways in which images are stored and manipulated in a digital machine.

  • • (Section 4.3) In this section, we introduce a way of thinking about images – as surfaces with varying height – which we will find to be a powerful way to describe both the properties of images as well as operations on those images.

    • Image Representations

    In this section, several ways to represent the information in an image are discussed. These representations include: iconic, functional, linear, probabilistic, and graphical representations. Note that in a digital image, the first dimension is columns and the second is rows. In a 3D digital image, the dimensions are columns, rows, and frames.

    Iconic Representations (An Image)

    An iconic representation of the information in an image is an image. Yeah, right; and a rose is a rose is a rose. When you see what we mean by functional, linear, and relational representations, you will realize we need a word for a representation that is itself a picture. In the following, we briefly describe 2D, 3D, and range images.

  • • 2D images: The familiar 2D image is the brightness image, also called luminance image. These include photographs; the things you are used to calling “images” or “pictures.” These might be color or grayscale. (Be careful with the words “black and white,” as that might be interpreted as “binary”). A shadow is a 2D binary image. We usually denote the brightness at a point < x, y > as f (x, y). Note: x and y could be either real numbers or integers. In the integer case, we are referring to discrete points in a sampled image. These points are called “pixels,” short for “picture elements.” In the case of real numbers we are usually thinking of the image as a function.

  • For the Instructor

  • Wesley E. Snyder, North Carolina State University, Hairong Qi, University of Tennessee
  • Book:
    Fundamentals of Computer Vision
    Published online:
    25 October 2017
    Print publication:
    28 September 2017, pp xv-xvi

  • Summary

    This is a first course in Computer Vision. It is intended for seniors or first-level graduate students in math-intensive curricula, such as electrical engineering, computer engineering, math, physics, or computer science.

    While this book provides a “foundation” in computer vision, a foundation in universitylevel mathematics is required for this book. We suggest that all students have the usual three-semester course in differential calculus, at least one course in differential equations, and one or two courses in concepts of matrices and linear algebra.

    The authors feel strongly that a student in Computer Vision should have a reasonably good grasp of what the computer is actually doing – and that means programming. While MATLAB is a fantastic research tool, and provides wonderful rendering tools, using MATLAB may prevent the student from gaining this insight into the basic operations (unless, of course, the student actually writes MATLAB code and doesn't use a toolbox). We prefer the student learn and use C or C++.

    We have a software package available with which we have had considerable success, described in Appendix C. It can be downloaded for free for MacOSX64, Linux64, and most versions of Windows, along with a lot of images, from www.cambridge.org/ 9781107184886. This package is, however, not required to use the book. The instructor may choose any software platform, including MATLAB.

    One style of teaching this course, the one we usually follow, is to have a number of small projects, roughly a week or two in duration, instead of a single end-of-class project.

    In teaching this course, the principal problems we have encountered are with students who don't know the difference between a compiler and a fishing rod, and students who think an eigenvalue is made with sugar and served with syrup. The emphasis on knowing linear algebra is very important.

    We also recommend that prior to taking this course, students take a class in image processing, in which they learn what a pixel is, what restoration does, and the difference between enhancement and filtering.

  • 5 - Kernel Operators

  • from Part II - Preprocessing
  • Wesley E. Snyder, North Carolina State University, Hairong Qi, University of Tennessee
  • Book:
    Fundamentals of Computer Vision
    Published online:
    25 October 2017
    Print publication:
    28 September 2017, pp 51-91

  • Summary

    You need boundaries … Even in our material creations, boundaries mark the most beautiful of places, between the ocean and the shore, between the mountains and the plains, where the canyon meets the river

    – Wm. Paul Young

    Introduction

    In this chapter, linear operations on images are investigated. The derivative, probably the most common linear operator, is considered first. That discussion is extended into edge detection, the result of applying derivative kernels on images. A variety of methods for accomplishing this objective are considered.

  • • (Section 5.2)We first define what makes a linear operator and explain the kernel operator, or sum of products, which is the type of linear operator that will appear most frequently in this book.

  • • (Section 5.3) We show in this section how to use vector representation of images to convert kernel operators to the matrix multiplication form in order to facilitate some analytical study.

  • • (Section 5.4) We focus on the discussion of derivatives, since it is probably the most common kernel operator used in Computer Vision applications. We discuss how to find the derivative kernel operators through the definition of derivatives, by function fitting, using vector representation of images, and taking derivatives of special blurring kernels.

  • • (Section 5.5) Applying derivative operators on images would result in edge images. We describe in this section the different types of edges and a popular edge detector, the Canny edge detector.

  • • (Section 5.6) The concept of scale space is explained and how the scale space is associated with the detection of edges at different scales.

  • • (Section 5.7) In Chapter 1, we briefly described the biological vision. Here, we revisit this issue and ask the question how human beings perform lower-level vision, i.e., edge detection. We introduce the Gabor filter, which is believed to well characterize the functionality of receptive fields in the visual cortex.

  • • (Section 5.8) We wrap up this chapter by performing an experimental study on the various types of derivative kernels in terms of their ability in detecting edges (both angle and magnitude) of different orientations.

  • Part I - Preliminaries

  • Wesley E. Snyder, North Carolina State University, Hairong Qi, University of Tennessee
  • Book:
    Fundamentals of Computer Vision
    Published online:
    25 October 2017
    Print publication:
    28 September 2017, pp 1-2

  • Summary

    In this part of the book, we start getting ready to do Computer Vision (CV). First, we briefly introduce biological vision and the biological motivation of Computer Vision. This is followed by a chapter describing how to write computer programs to process images. We then provide a chapter of math. The emphasis in that chapter is linear algebra, as that is the mathematical discipline most used in CV. We also touch briefly on probability and function minimization.

    After we have the human prepared by taking the prerequisites and reviewing the math, we need for that human to know what an image actually is. It turns out that the word “image” has a number of different meanings in different contexts, and Chapter 4 discusses them.

  • Part II - Preprocessing

  • Wesley E. Snyder, North Carolina State University, Hairong Qi, University of Tennessee
  • Book:
    Fundamentals of Computer Vision
    Published online:
    25 October 2017
    Print publication:
    28 September 2017, pp 49-50

  • Summary

    When the authors first started in Computer Vision, our intention was to write programs using the highest level, most elegant, most sophisticated Artificial Intelligence methods known. Of course, nothing worked.

    Images are never what you expect. Real images all have noise. Even a perfect digital image is sampled, and sampling itself introduces a type of noise. Then there is blur and other distortions.

    We begin this Part of the book by looking at the issue of finding edges in noisy images. That chapter will not only show how to find edges; it will introduce some other basic topics in image manipulation such as convolution.

    Then, we move into removing noise. Blurring an image will certainly remove noise. Of course, it will remove image content also. The trick is to remove the noise but preserve image details, and that topic is discussed in the next chapter.

    The final topic in this Part is morphology, a collection of nonlinear methods for erasing small details and closing gaps. The distance transform, a compact and useful representation for the information in an image, is also included in the morphology chapter.

Biomedical Image Analysis
  • Statistical and Variational Methods
  • Aly A. Farag
  • Published online:
    05 November 2014
    Print publication:
    30 October 2014
  • Ideal for classroom use and self-study, this book explains the implementation of the most effective modern methods in image analysis, covering segmentation, registration and visualisation, and focusing on the key theories, algorithms and applications that have emerged from recent progress in computer vision, imaging and computational biomedical science. Structured around five core building blocks - signals, systems, image formation and modality; stochastic models; computational geometry; level set methods; and tools and CAD models - it provides a solid overview of the field. Mathematical and statistical topics are presented in a straightforward manner, enabling the reader to gain a deep understanding of the subject without becoming entangled in mathematical complexities. Theory is connected to practical examples in x-ray, ultrasound, nuclear medicine, MRI and CT imaging, removing the abstract nature of the models and assisting reader understanding.

  • 15 - Statistical models of shape and appearance

  • from Part V - Image analysis tools
  • Aly A. Farag, University of Louisville, Kentucky
  • Book:
    Biomedical Image Analysis
    Published online:
    05 November 2014
    Print publication:
    30 October 2014, pp 417-457

  • Summary

    Introduction

    In this chapter, statistical models, derived from the shape and texture of an object in an image or volume, are studied. Statistical shape and appearance models can capture patterns of variability in shape and gray-level appearance. They form the basis of two of the most powerful tools for object analysis – active shape models (ASM) and active appearance models (AAM) – and are very popular in the computer vision and biomedical imaging analysis literature. This chapter reviews the basic foundation of these two statistical models and provides illustrative examples of their effectiveness in object modeling. The chapter builds upon various ideas studied in previous chapters.

    Statistical shape models

    The shape of an object can be represented by a set of n points, which can be in any dimension (i.e., 2D or 3D). Adopting Kendall’s definition [15.1][15.2], shape is formally defined as:

    DEFINITION 15.1 A shape embodies all the geometrical information that remains when location, scale, and rotational effects are filtered out from an object. ■

  • 14 - Variational methods for shape registration

  • from Part V - Image analysis tools
  • Aly A. Farag, University of Louisville, Kentucky
  • Book:
    Biomedical Image Analysis
    Published online:
    05 November 2014
    Print publication:
    30 October 2014, pp 387-416

  • Summary

    Variational methods are based on continuous modelling of input data through the use of partial differential equations (PDE), which benefits from the well-developed theory and numerical methods on PDEs. A novel variational framework for global-to-local shape registration is presented. A new sum-of-squared-differences (SSD) criterion, which measures the disparity between the “implicit” representations of the input shapes, is introduced to recover the global alignment parameters. This new criterion has some advantages over existing ones in accurately handling scale variations. Complementary to the global registration field, the local deformation field is explicitly established between two globally aligned shapes, by minimizing an energy functional which incrementally updates the displacement field while keeping the corresponding implicit representation of the globally warped source shape as close as possible to a “signed distance” function. The optimization is performed under regularization constraints that enforce the smoothness of the recovered deformations. The overall process leads to a coupled set of equations that are simultaneously solved through a gradient descent scheme. The finite element (FE) approach for solving PDEs may be used to validate the performance of the shape registration technique. This chapter provides a holistic approach for shape registration.

    Introduction

    The process of registering shapes is based on three main components, namely (1) the way to represent the shapes, (2) the transformation model, and (3) the mathematical framework selected to recover the registration parameters. The following section briefly reviews each of these components.

  • 10 - Variational approaches and level sets

  • from Part IV - Variational approaches and level sets
  • Aly A. Farag, University of Louisville, Kentucky
  • Book:
    Biomedical Image Analysis
    Published online:
    05 November 2014
    Print publication:
    30 October 2014, pp 275-294

  • Summary

    Objects captured in a scene may intersect and occlude each other in the field of view of an imaging sensor, and may suffer from uncertainties in the imaging process. The object shape may be described by its outline (contour). There exists a rich image analysis literature on approaches to extract the contours of objects. This chapter will focus on deformable models and level set methods to extract object contours. Active contours are curves that deform within an object representation (e.g., a digital image) in order to recover the object shape. They are classified as parametric or geometric, according to their representation and implementation. In particular, parametric active contours are represented explicitly in terms of parameterized curves in a Lagrangian formulation (e.g. [10.1],[10.2]). On the other hand, geometric active contours are represented implicitly as level sets of 2D distance functions, which evolve according to an Eulerian formulation. They are based on the theory of curve evolution implemented via level set techniques. Parametric active contours are the older of the two formulations.

    Geometric active contours, also known as level set methods (LSM), handle topological changes during curve evolution (e.g. [10.3]). They describe an object contour by considering it as a slice through a higher-dimensional object known as the level set function. The contour intersects the level set function at the x–y plane, which is known as the zero-level set. Contour motion normal to the level set is given by a Hamilton–Jacobi partial differential equation (PDE). This chapter discusses the mathematical foundation of classical deformable models and level sets. LSM can be used for 2D or 3D object representations, and can address various topological and geometrical characteristics of the objects. These methods lead to solutions in the continuous domain [10.4][10.5]. Deformable models and LSM have been successful in image analysis, especially image segmentation and registration [10.6–10.11].

  • 11 - Segmentation: statistical approach

  • from Part V - Image analysis tools
  • Aly A. Farag, University of Louisville, Kentucky
  • Book:
    Biomedical Image Analysis
    Published online:
    05 November 2014
    Print publication:
    30 October 2014, pp 297-315

  • Summary

    Introduction

    Segmentation is a fundamental step in understanding images. As image formation involves various sensor types, and objects vary in complexities of shape, spatial support, texture, and color, and the circumstances of the scenes may not be fully understood in advance, various approaches and algorithms for image segmentation have evolved over the years. In this book we address the basic issues in image segmentation: this chapter and the next will consider statistical and variational calculus approaches for segmentation. The focus will be on general frameworks which can be altered according to the specifics of the objects in the image, and the models used.

    This chapter describes an unsupervised maximum-a-posteriori (MAP) based segmentation framework of N-dimensional multimodal images, in which objects occupy distinct, albeit overlapping, domains in the intensity histogram. The input image and its desired map (labeled image) are described by a joint Markov–Gibbs random field (MGRF) model of independent image signals and interdependent region labels. These models were discussed in Chapter 6. We deploy the kernel approach of Chapter 7 to model the joint and marginal probability densities of objects from the gray-level histogram, which incorporates a generalized linear combination of Gaussians (LCG), where the weights of the kernels may take positive and negative values, while maintaining the positivity and integrability constraints. The number of classes is estimated using a maximum likelihood approach applied to the LCG model. An approach is devised for MGRF model identification based on region characteristics. The segmentation process is conducted by using the LCG-model to provide an initial segmentation (pre-labeled image), and then a subsequent algorithm iteratively refines the labeled image using the MGRF. The convergence of the algorithm is examined, and a sensitivity analysis is performed to quantify its robustness with respect to initialization, improper estimation of the number of classes, and discontinuities in the objects. We illustrate the effectiveness of this approach for modeling and segmentation of objects (structures) in synthetic and biomedical images.

  • 3 - Biomedical imaging modalities

  • from Part I - Signals and systems, image formation, and image modality
  • Aly A. Farag, University of Louisville, Kentucky
  • Book:
    Biomedical Image Analysis
    Published online:
    05 November 2014
    Print publication:
    30 October 2014, pp 39-76

  • Summary

    Introduction

    Methods of examining the anatomy and function of living organisms have advanced immensely over the past century. Biomedical imaging has evolved in terms of types of imaging system (modalities) and capabilities, and has improved our understanding of biological systems. It has affected the quality of our lives by transforming various medical practices from arts to science, enabling better healthcare administration, and leading on average to longer and healthier lives. The technology also has an economic impact: vast numbers of technical professionals (chemists, mathematicians, physicists, engineers, and computer scientists) work in companies making biomedical imaging devices, or in research laboratories and hospitals. One chapter cannot hope to cover a vibrant and ever-dynamic field; we will merely scratch the surface in understanding the process of image formation in some of the common imaging modalities. There are more specialized books, periodicals, and manufacturers’ reports that should be consulted by readers interested in delving into the field of biomedical imaging.

    This chapter serves as a brief tour of a field of ever-expanding diversity and capabilities. The focus, however, will be on the imaging modalities that have guided the development of the basic theories and approaches to image analysis covered in the subsequent chapters of this book. We concentrate on image analysis approaches that have been well-studied for images from two broad categories of imaging sensors: those based on ionizing radiations (e.g. X-rays and computed tomography) and those based on magnetization (e.g. magnetic resonance imaging). Positron emission tomography (PET), ultrasound imaging, laser imaging, thermal infrared imaging and other modalities are also important, but this chapter will not cover all of these.

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