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1156 results in Computer Graphics, Image Processing and Robotics

Page 14 of 58

Media and Radio Signal Processing for Mobile Communications
  • Kyunghun Jung, Russell M. Mersereau
  • Published online:
    23 March 2018
    Print publication:
    19 April 2018
  • Get to grips with the principles and practice of signal processing used in mobile communications systems. Focusing particularly on speech, video, and modem signal processing, pioneering experts employ a detailed, top-down analytical approach to outline the network architectures and protocol structures of multiple generations of mobile communications systems, identify the logical ranges where media and radio signal processing occur, and analyze the procedures for capturing, compressing, transmitting, and presenting media. Chapters are uniquely structured to show the evolution of network architectures and technical elements between generations up to and including 5G, with an emphasis on maximizing service quality and network capacity through re-using existing infrastructure and technologies. Implementation examples and data taken from commercial networks provide an in-depth insight into the operation of real mobile communications systems, including GSM, cdma2000, W-CDMA, LTE, and LTE-A, making this a practical, hands-on guide for both practicing engineers and graduate students in wireless communications.

  • 6 - Noise Removal

  • 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 92-118

  • Summary

    To change and to change for the better are two different things.

    – German proverb.

    Introduction

    In a photosensitive device such as a phototransistor or charge-coupled device, an incidence of a photon of light may (probabilistically) generate an electronic charge. The number of charges produced should be proportional to the photons per second striking the device. However, the presence of heat (anything above absolute zero) will also randomly produce charges, and therefore signal. Such a signal is called dark current because it is a signal that is produced by a camera, even in the dark. Dark current is one of several phenomena that result in random fluctuations to the output of a camera that we call noise. The nature of noise is closely related to the type of sensor. For example, devices that count emissions of radioactive particles are corrupted by a noise that has a Poisson distribution rather than the Gaussian noise of dark current.

    In this chapter, techniques are developed that remove noise and degradations so that features can be derived more cleanly for segmentation. We will introduce each topic in one dimension, to allow the student to better understand the process, and then extend that concept to two dimensions. This is covered in the following sections:

  • • (Section 6.2) The noise in the image can be reduced simply by smoothing. However, the smoothing process also blurs the edges. This section introduces the subject of reducing the noise while at the same time preserving edges, i.e., edge-preserving smoothing.

  • • (Section 6.3) An intuitive idea in designing edge-preserving smoothing is that smoothing should be associated with a weight according to the local image data where it is applied. And the weight should be large if two pixels are close spatially and have similar photometric values. Otherwise, the weight should be small. The bilateral filter is an algorithm that realizes this ad hoc “good idea.”

  • • (Section 6.4) Diffusion is described here to pose the denoising problem as the solution to a partial differential equation (PDE). The challenge is how to find a PDE that causes blurring except at edges.

  • • (Section 6.5) The Maximum A Posteriori probability (MAP) algorithm is discussed to show how to formulate noise removal as a minimization problem. Here, the challenge is to find an objective function whose minimum is the desired result.

  • 1 - Computer Vision, Some Definitions, and Some History

  • 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 3-10

  • Summary

    No object is mysterious. The mystery is your eye.

    – Elizabeth Bowen

    Introduction

    There are two fundamentally different philosophies concerning understanding the brain. (1) Understand the brain first. If we can understand how the brain works, we can build smart machines. (2) Using any technique we can think of, make a smart machine. If we can accomplish that, it will give us some hints about how the brain works. This book is all about the second approach, although it draws from current understanding of biological computing. In this chapter, however, we define a few terms, introduce the greater localglobal problem, and then give a very brief introduction to the function of the mammalian brain.

  • • (Section 1.2) From signal and systems perspective, we describe the differences between Computer Vision and some other closely related fields of studies, including, e.g., image processing and pattern recognition.

  • • (Section 1.3) Since almost all problems in Computer Vision involve the issue of localness versus globalness, we briefly explain the “local-global” problem and the “consistency” principle used to solve this problem.

  • • (Section 1.4) Computer Vision is deep-rooted in biological vision. Therefore, in this section, we discuss the biological motivation of Computer Vision and some amazing discoveries from the study of the human visual system.

    • Some Definitions

    Computer Vision is the process whereby a machine, usually a digital computer, automatically processes an image and reports “what is in the image.” That is, it recognizes the content of the image. For example, the content may be a machined part, and the objective may be not only to locate the part but to inspect it as well.

    Students tend to get confused by other terms that often appear in the literature, such as Image Processing, Machine Vision, Image Understanding, and Pattern Recognition.

    We can divide the entire process of Image Processing into Low-Level Image Processing and High-Level Image Processing. If we interpret these processes from signal and systems perspective, it is more clear to describe their difference and similarity from the format of input/output of the system. When a Low-Level Image Processing system processes an input image, the output is still an image, but a somewhat different image. For example, it may be an image with noise removed, an image that does not take as much storage space as the input image, an image that is sharper than the input image, etc.

  • 12 - Relating to Three Dimensions

  • from Part IV - The 2D Image in a 3D World
  • 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 303-349

  • Summary

    I've always been passionate about geometry and the study of three-dimensional forms.

    – Erno Rubik

    Introduction

    Most of the images we see are projections of surfaces in the three-dimensional world around us. They result from light reflected off surfaces in that 3D world, passing through the lens of a camera, and intersecting the focal plane of the camera. These images that result from light reflected in this way are called “luminance” or “brightness” images in this book.

    What was not described earlier in this book is the relationship between the 3D world and 2D images, including matching of one to another. We begin by reviewing the geometry of a simple projective camera and relating it to position of points in three dimensions. What we would really like is a range image from every scene, but that isn't always feasible, so we look at several aspects of the 2D–3D relationship:

  • • (Section 12.2) It is necessary to determine the 3D position of a point in space that is seen by two cameras, assuming the two cameras are known. This is the problem commonly known as stereopsis. When we say a camera is “known” we mean we know where it is, which way it is pointing, and all its internal parameters like focal length, resolution, and others.

  • • (Section 12.3) Actually it is not really necessary to know all about the cameras. Almost all the relevant information about both cameras can be determined if there are several points in each camera view that can be put into correspondence. An adequate solution to this problem leads to a wonderful little matrix called the fundamental matrix that contains all we need to know for the two-camera problem. Underlying this work is the correspondence problem, the problem of identifying which point in one image corresponds to which point in the other image. Finding a robust solution to the correspondence problem may be difficult.

  • • (Section 12.4) Once we have an approach to the correspondence problem, we can do partial matching of images and image stitching.

  • • (Section 12.5) If, instead of two cameras, we have one camera and a controllable light source, we can still find the 3D location of points in space. We address controllable lighting and how to achieve range imaging in this context.

  • 3 - Review of Mathematical Principles

  • 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 16-38

  • Summary

    Practical problems require good math.

    – R. Chellappa

    Introduction

    This chapter is a review of several of the topics that are prerequisite for use of this book as a text. The student should have had an undergraduate calculus experience equivalent to about three semesters and some exposure to differential equations and partial differential equations. The student should have coursework containing concepts from probability and statistics, including prior probabilities, conditional probability, Bayes’ rule, and expectations. Finally, and very important, the student should have strong undergraduate-level training in linear algebra.

    This chapter reviews and refreshes many of the concepts in those courses, but only as a review, not as a presentation of totally new material.

    • (Section 3.2) We briefly review important concepts in linear algebra, including various vector and matrix operations, the derivative operators, eigendecomposition, and its relationship to singular value decomposition.

    • (Section 3.3) Since almost all Computer Vision topics can be formulated as minimization problems, in this section, we briefly introduce function minimization, and discuss gradient descent and simulated annealing, the two minimization techniques that can lead to local and global minima, respectively.

    • (Section 3.4) In Computer Vision, we are often interested in the probability of certain measurement occurring. In this section, we briefly review concepts like probability density functions and probability distribution functions.

    A Brief Review of Linear Algebra

    In this section, we very briefly review vector and matrix operations. Generally, we denote vectors in boldface lowercase, scalars in lowercase italic Roman, and matrices in uppercase Roman.

    Vectors

    Vectors are always considered to be column vectors. If we need to write one horizontally for the purpose of saving space in a document, we use transpose notation. For example, we denote a vector that consists of three scalar elements as:

    The Inner Product

    The inner product of two vectors is a scalar, c = xTy. Its value is the sum of products of the corresponding elements of the two vectors:

    You will also sometimes see the notation <x,y> used for inner product. We do not like this because it looks like an expected value of a random variable. One sometimes also sees the “dot product” notation x · y for inner product.

  • Preface

  • 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 xiii-xiv

  • Summary

    This book introduces the fundamental principles of Computer Vision to the advanced undergraduate or first-year graduate student in mathematics, computer science, or engineering.

    The book is deliberately informal. The authors attempt to keep the student interested and motivated to continue reading. The student is often addressed directly, as if the student and the authors were in a classroom together. The style is somewhat casual, the authors use the first person frequently, the passive voice is seldom used, and the occasional joke may appear.

    The foundations described in the title of this book take two forms: mathematical principles and algorithmic concepts. The principles and concepts are taught together, by describing a computer vision problem, e.g., segmentation, describing an algorithm that could solve that problem, and explaining the mathematical principles underlying the algorithm.

    These mathematical principles include

    Linear Operators Taught through a variety of applications, including:

    Basis Functions Taught through edge detectors

    Gaussian Convolution Taught through development of Gaussian edge kernels

    Constrained Optimization Taught through finding optimal edge detection kernels and through principal components

    The Pseudoinverse Taught through explaining photometric stereo

    Scale Taught through development of Gaussian edge kernels.

    Nonlinear Operators Taught through mathematical morphology.

    Effects of Sampling Taught by illustrating the use of small kernels for determining orientation.

    Use of Optimization Taught through development of noise removal algorithms, adaptive contours for segmentation and graph cuts.

    Use of Consistency Taught through Hough-like algorithms, through shape matching, and projection onto a manifold.

    Projective Geometry Taught through shape from motion and shape from X algorithms.

    These concepts are organized in a progression of levels, moving from pixel-level operations such as noise removal, through edge detection, segmentation, and shape description, and finally to recognition. At each level in the progression, the student learns what specific terminology means, what a good application of the concept to an image does, and one or more approaches to solving the application problem.

    Almost all the images used as examples in the book are available for download. When one of these figures is used, the figure caption gives the name of the image.

  • 10 - Representing and Matching Shape

  • 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 218-266

  • Summary

    Shape is what is left when the effects associated with translation, scaling, and rotation are filtered away.

    – David Kendall

    Introduction

    In this chapter, we assume a successful segmentation, and explore the question of characterization of the resulting regions. We begin by considering two-dimensional regions that are denoted by each pixel in the region having value 1 and all background pixels having value 0.We assume only one region is processed at a time, since in studying segmentation, we learned how to realize these assumptions.

    When thinking about shapes, and measures for shapes, it is important to keep in mind that certain measures may have invariance properties. That is, a measure may remain the same if the object is (for example) rotated. Consider the height of a person in a picture – if the camera rotates, the apparent height of the person will change, unless, of course, the person rotates with the camera.

    The common transformations considered in this chapter are those described by some linear operation on the shape matrix, discussed in section 4.2.3.

    In the remainder of this chapter, we will be constantly thinking about operations that exhibit various invariances, and can be used to match shapes of regions.

  • • (Section 10.2) To understand invariances, we must first understand the deformations that may alter the shape of a region, and most of those can be described by matrix operations.

  • • (Section 10.3) One particularly important matrix is the covariance matrix of the distribution of points in a region, since the eigenvalues and eigenvectors of that matrix describe shape in a very robust way.

  • • (Section 10.4) In this section, we introduce some important features used to describe a region. We start from some simple properties of a region like perimeter, diameter, and thinness. We then extend the discussion to some invariant features (to various linear transformations) like moments, chain codes, Fourier descriptors, and the medial axis.

  • • (Section 10.5) Since, in earlier sections, we have represented the regions by sets of numbers called features, in this section, we discuss how to match such sets of numbers.

  • 13 - Developing Computer Vision Algorithms

  • from Part IV - The 2D Image in a 3D World
  • 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 350-352

  • Summary

    Education is what remains after one has forgotten everything one learned in school.

    – Albert Einstein

    We conclude the book with a look back in the context of how one develops good algorithms to solve Computer Vision problems. The steps are listed in order, as much as possible, with reference to materials and examples in the book.

    The approach is explained through an example: Suppose you need to develop an algorithm to construct a panorama from two overlapping images. This requires that you find some way to transform coordinates in one image to appropriate coordinates in the next image, as described in Chapter 12. (See Figure 13.1.)

    Know the literature If you are working on a problem that you think is important, chances are somebody else has also worked on it. Since the advent of Web searching, it has become easier to search, but don't limit your searches to Google. It's OK if you spend several days looking in the library. Looking at actual paper copies of old journal papers isn't necessarily a bad thing. After all, you plan to spend months or years on this project. Some papers were written before Web searching [13.2]. Often, you can be fortunate enough to find that someone else has done a good literature survey for you. For example, in the topic of the shape from motion, [13.3] and [13.1] thoroughly teach the relevant material.

    Form an Objective Function In Chapter 6, we saw one example of finding an image that is the solution to an optimization problem.We found images that resembled the input image but also had some other desirable properties. In Chapter 5 we derived convolution kernels by finding best fits to data. In Chapter 12 objective functions were explicitly used twice.

    In some rare instances, it isn't possible to set up a problem in terms of an optimization problem, but it's a good way to start.

    Do the Math Correctly Once you have set up an objective function, you need to minimize it. For that, you often need a gradient. Can you find the gradient analytically as in section 6.5.1, or must you use numerical methods to estimate the gradient? In Chapter 12, we solved for a homography by using two images. But even if the math is correct, is it a valid approach?

Page 14 of 58