14-04-2011, 12:19 PM
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1.1 Introduction:
A digital image is a representation of a two-dimensional signal using ones and zeros (binary). Depending on whether or not the image resolution is fixed, it may be of vector or raster type. Without qualifications, the term "digital image" usually refers to raster images also called bitmap images
An image may be defined as a two-dimensional function f(x ,y ) where x and y are spatial(plane) co-ordinates, and the amplitude of f at any pair of coordinates(x, y) called the intensity or gray level of the image at that point. When x, y and the amplitude values of f are all finite, discrete quantities, We call the image a digital image.
Raster image types:
Each pixel of a raster image is typically associated to a specific 'position' in some 2D region, and has a value consisting of one or more quantities (samples) related to that position. Digital images can be classified according to the number and nature of those samples:
• binary
• grayscale
• 1color
• false-color
• multi-spectral
• thematic
• picture function
The term digital image is also applied to data associated to points scattered.
1.2 Digital Image Processing:
The field of digital image processing refers to processing digital images by Means of a digital computer. A digital image is composed of a finite number of elements, each of which has a particular location and value. This elements are referred to as picture elements, image elements, and pixels. Pixels is the term most widely used to denote the elements of digital image.
1.2.1 Fundamental Steps In Digital Image Processing:
Image Enhancement:
Image enhancement is among the simplest and most appealing areas of digital image processing. Basically, the idea behind enhancement techniques is to bring out detail that is obscured or simply to highlight certain features of interest in an image.
A familiar example of enhancement is when we increase the contrast of an image because,it is important to keep in mind that enhancement is a very subjective area of image processing.
Image Restoration:
Image Restoration is an area that also deals with improving the appearance of an image. However, unlike enhancement, which is subjective, image restoration techniques tend to be based on mathematical or probabilistic models of image Degradation.
Color Image Processing:
Color image processing is an area that has been gaining in importance because of the significant Increase In the use of digital image over the internet.
Wavelets:
Wavelets are the foundation for representing images in various degrees of resolution. In particular, this will be used for image data compression and for pyramidal representation, in which images are subdivided successively into smaller Regions.
Compression:
As the name implies, deals with techniques for reducing the storage required to save an image, or the bandwidth required to transmit it. Although storage technology has improved significantly over the past decade, the same cannot be said for transmission capacity. Image
compression is used familiar to most users of computers in the form of image file extensions, Such as the file extension used I the JPEG(joint photographic experts group).
1.2.2 Applications of Digital Image Processing:
• Remote sensing via satellites & space crafts
• Image transmission &storage for business applications
• Medical processing
• Radar & sonar image processing
• Robotics
Exampl1es of fields that use digital image processing
• gama ray imaging
• X-ray imaging
• Imaging in ultra violet band
• Imaging in visible & infrared bands
• Imaging in the microwave bands
• Imaging in radio bands
1.3 Aim of the project:
The main aim of any encoder scheme is to compress the number of data bits that could be transmitted into the channel. Mainly jpeg encoder tries to remove three types of redundancies that occur in an image namely coding redundancy, psychovisual redundancy and inter pixel redundancies.
1.4 Problem statement:
The main problem with jpeg encoder is that it can be applied to stationary images. How ever we need in certain circumstances to apply it for non stationary images where we need to lie upon discrete wavelet transforms.
1.5 ORGANIZATION OF THE PROJECT:
Chapter 1 presents introduction to image processing, fundamental steps, applications and example areas image processing. Finally aim and problem statements are discussed.
Chapter 2 provides the literature survey on fourier transform, discrete fourier transform and fast fourier transform and their properties.
Chapter 3 provides the various concepts of image compression, types of image compression, proposed model block diagram and explanation of that block diagram.
Chapter 4 focuses the Implementation of jpeg encoder module wise such as DCT, quantiser, entropy encoding .
Chapter 5 presents the some of results obtained after application of input images and corresponding reconstructed images.
Chapter 6 gives Applications and usage of JPEG Encoder
Chapter 7 gives summary of the work carried, this includes conclusions, performance analysis.
Chapter 8 represents scope for future work.
Chapter 9 References.
Appendix A focuses on the VLSI Design Flow.
Appendix B Source code
2. LITERATURE SURVEY
2.1 Introduction to Fourier Transform:
In, the Fourier transform (often abbreviated FT) is an operation that transforms one complex-valued function of a real variable into another. In such applications as signal processing, the domain of the original function is typically time and is accordingly called the time domain. That of the new function is frequency, and so the Fourier transform is often called the frequency domain representation of the original function. It describes which frequencies are present in the original function. This is analogous to describing a chord of music in terms of the notes being played. In effect, the Fourier transform decomposes a function into oscillatory functions. The term Fourier transform refers both to the frequency domain representation of a function, and to the process or formula that "transforms" one function into the other.
The Fourier transform and its generalizations are the subject of Fourier analysis. In this specific case, both the time and frequency domains are unbounded linear continua. It is possible to define the Fourier transform of a function of several variables, which is important for instance in the physical study of wave motion and optics. It is also possible to generalize the Fourier transform on discrete structures such as finite groups, efficient computation of which through a fast Fourier transform is essential for high-speed computing.
Definition:
There are several common conventions for defining the Fourier transform of an integrable function ƒ : R → C (Kaiser 1994). This article will use the definition:
for every real number ξ.
When the independent variable x represents time (with SI unit of seconds), the transform variable ξ represents frequency (in hertz). Under suitable conditions, ƒ can be reconstructed from by the inverse transform
for every real number x.
Introduction: The motivation for the Fourier transform comes from the study of Fourier series. In the study of Fourier series, complicated periodic functions are written as the sum of simple waves mathematically represented by sines and cosines. Due to the properties of sine and cosine it is possible to recover the amount of each wave in the sum by an integral. In many cases it is desirable to use Euler's formula, which states that e2πiθ = cos 2πθ + i sin 2πθ, to write Fourier series in terms of the basic waves e2πiθ. This has the advantage of simplifying many of the formulas involved and providing a formulation for Fourier series that more closely resembles the definition followed in this article. This passage from sines and cosines to complex exponentials makes it necessary for the Fourier coefficients to be complex valued. The usual interpretation of this complex number is that it gives you both the amplitude (or size) of the wave present in the function and the phase (or the initial angle) of the wave. This passage also introduces the need for negative "frequencies". If θ were measured in seconds then the waves e2πiθ and e−2πiθ would both complete one cycle per second, but they represent different frequencies in the Fourier transform. Hence, frequency no longer measures the number of cycles per unit time, but is closely related.
1.1 Introduction:
A digital image is a representation of a two-dimensional signal using ones and zeros (binary). Depending on whether or not the image resolution is fixed, it may be of vector or raster type. Without qualifications, the term "digital image" usually refers to raster images also called bitmap images
An image may be defined as a two-dimensional function f(x ,y ) where x and y are spatial(plane) co-ordinates, and the amplitude of f at any pair of coordinates(x, y) called the intensity or gray level of the image at that point. When x, y and the amplitude values of f are all finite, discrete quantities, We call the image a digital image.
Raster image types:
Each pixel of a raster image is typically associated to a specific 'position' in some 2D region, and has a value consisting of one or more quantities (samples) related to that position. Digital images can be classified according to the number and nature of those samples:
• binary
• grayscale
• 1color
• false-color
• multi-spectral
• thematic
• picture function
The term digital image is also applied to data associated to points scattered.
1.2 Digital Image Processing:
The field of digital image processing refers to processing digital images by Means of a digital computer. A digital image is composed of a finite number of elements, each of which has a particular location and value. This elements are referred to as picture elements, image elements, and pixels. Pixels is the term most widely used to denote the elements of digital image.
1.2.1 Fundamental Steps In Digital Image Processing:
Image Enhancement:
Image enhancement is among the simplest and most appealing areas of digital image processing. Basically, the idea behind enhancement techniques is to bring out detail that is obscured or simply to highlight certain features of interest in an image.
A familiar example of enhancement is when we increase the contrast of an image because,it is important to keep in mind that enhancement is a very subjective area of image processing.
Image Restoration:
Image Restoration is an area that also deals with improving the appearance of an image. However, unlike enhancement, which is subjective, image restoration techniques tend to be based on mathematical or probabilistic models of image Degradation.
Color Image Processing:
Color image processing is an area that has been gaining in importance because of the significant Increase In the use of digital image over the internet.
Wavelets:
Wavelets are the foundation for representing images in various degrees of resolution. In particular, this will be used for image data compression and for pyramidal representation, in which images are subdivided successively into smaller Regions.
Compression:
As the name implies, deals with techniques for reducing the storage required to save an image, or the bandwidth required to transmit it. Although storage technology has improved significantly over the past decade, the same cannot be said for transmission capacity. Image
compression is used familiar to most users of computers in the form of image file extensions, Such as the file extension used I the JPEG(joint photographic experts group).
1.2.2 Applications of Digital Image Processing:
• Remote sensing via satellites & space crafts
• Image transmission &storage for business applications
• Medical processing
• Radar & sonar image processing
• Robotics
Exampl1es of fields that use digital image processing
• gama ray imaging
• X-ray imaging
• Imaging in ultra violet band
• Imaging in visible & infrared bands
• Imaging in the microwave bands
• Imaging in radio bands
1.3 Aim of the project:
The main aim of any encoder scheme is to compress the number of data bits that could be transmitted into the channel. Mainly jpeg encoder tries to remove three types of redundancies that occur in an image namely coding redundancy, psychovisual redundancy and inter pixel redundancies.
1.4 Problem statement:
The main problem with jpeg encoder is that it can be applied to stationary images. How ever we need in certain circumstances to apply it for non stationary images where we need to lie upon discrete wavelet transforms.
1.5 ORGANIZATION OF THE PROJECT:
Chapter 1 presents introduction to image processing, fundamental steps, applications and example areas image processing. Finally aim and problem statements are discussed.
Chapter 2 provides the literature survey on fourier transform, discrete fourier transform and fast fourier transform and their properties.
Chapter 3 provides the various concepts of image compression, types of image compression, proposed model block diagram and explanation of that block diagram.
Chapter 4 focuses the Implementation of jpeg encoder module wise such as DCT, quantiser, entropy encoding .
Chapter 5 presents the some of results obtained after application of input images and corresponding reconstructed images.
Chapter 6 gives Applications and usage of JPEG Encoder
Chapter 7 gives summary of the work carried, this includes conclusions, performance analysis.
Chapter 8 represents scope for future work.
Chapter 9 References.
Appendix A focuses on the VLSI Design Flow.
Appendix B Source code
2. LITERATURE SURVEY
2.1 Introduction to Fourier Transform:
In, the Fourier transform (often abbreviated FT) is an operation that transforms one complex-valued function of a real variable into another. In such applications as signal processing, the domain of the original function is typically time and is accordingly called the time domain. That of the new function is frequency, and so the Fourier transform is often called the frequency domain representation of the original function. It describes which frequencies are present in the original function. This is analogous to describing a chord of music in terms of the notes being played. In effect, the Fourier transform decomposes a function into oscillatory functions. The term Fourier transform refers both to the frequency domain representation of a function, and to the process or formula that "transforms" one function into the other.
The Fourier transform and its generalizations are the subject of Fourier analysis. In this specific case, both the time and frequency domains are unbounded linear continua. It is possible to define the Fourier transform of a function of several variables, which is important for instance in the physical study of wave motion and optics. It is also possible to generalize the Fourier transform on discrete structures such as finite groups, efficient computation of which through a fast Fourier transform is essential for high-speed computing.
Definition:
There are several common conventions for defining the Fourier transform of an integrable function ƒ : R → C (Kaiser 1994). This article will use the definition:
for every real number ξ.
When the independent variable x represents time (with SI unit of seconds), the transform variable ξ represents frequency (in hertz). Under suitable conditions, ƒ can be reconstructed from by the inverse transform
for every real number x.
Introduction: The motivation for the Fourier transform comes from the study of Fourier series. In the study of Fourier series, complicated periodic functions are written as the sum of simple waves mathematically represented by sines and cosines. Due to the properties of sine and cosine it is possible to recover the amount of each wave in the sum by an integral. In many cases it is desirable to use Euler's formula, which states that e2πiθ = cos 2πθ + i sin 2πθ, to write Fourier series in terms of the basic waves e2πiθ. This has the advantage of simplifying many of the formulas involved and providing a formulation for Fourier series that more closely resembles the definition followed in this article. This passage from sines and cosines to complex exponentials makes it necessary for the Fourier coefficients to be complex valued. The usual interpretation of this complex number is that it gives you both the amplitude (or size) of the wave present in the function and the phase (or the initial angle) of the wave. This passage also introduces the need for negative "frequencies". If θ were measured in seconds then the waves e2πiθ and e−2πiθ would both complete one cycle per second, but they represent different frequencies in the Fourier transform. Hence, frequency no longer measures the number of cycles per unit time, but is closely related.
