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DIGITAL IMAGE PROCESSING
(R15A0426)
Lecture Notes
B.TECH
(IV YEAR – I SEM)
Prepared by:
Dr. P. LAKSHMI DEVI, Professor
Dr. N. SUBASH, Assistant Professor
Department of Electronics and Communication Engineering
MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY
(Autonomous Institution – UGC, Govt. of India)
Recognized under 2(f) and 12 (B) of UGC ACT 1956 (AffiliatedtoJNTUH,Hyderabad,ApprovedbyAICTE-AccreditedbyNBA&NAAC–‘A’Grade-ISO9001:2015Certified) Maisammaguda,Dhulapally(PostVia.Kompally),Secunderabad–500100,TelanganaState,India
MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY
IV Year B. Tech. ECE-I Sem L T/P/D C 4 1/-/- 3 CORE ELECTIVE - IV (R15A0426) DIGITAL IMAGE PROCESSING Course Objectives: The course objectives are:
- Provide the student with the fundamentals of digital image processing
- Give the students a taste of the applications of the theories taught in the subject. This will be achieved through the project and some selected lab sessions.
- Introduce the students to some advanced topics in digital image processing.
- Give the students a useful skill base that would allow them to carry out further study should they be interested and to work in the field. UNIT I Digital image fundamentals & Image Transforms :- Digital Image fundamentals, Sampling and quantization, Relationship between pixels. Image Transforms: 2 - D FFT, Properties. Walsh transform, Hadamard Transform, Discrete cosine Transform, Discrete Wavelet Transform. UNIT II Image enhancement (spatial domain) : Introduction, Image Enhancement in Spatial Domain, Enhancement Through Point Operation, Types of Point Operation, Histogram Manipulation, gray level Transformation, local or neighborhood operation, median filter, spatial domain high- pass filtering. Image enhancement (Frequency domain): Filtering in Frequency Domain, Obtaining Frequency Domain Filters from Spatial Filters, Generating Filters Directly in the Frequency Domain, Low Pass(smoothing) and High Pass (sharpening) filters in Frequency Domain UNIT III Image Restoration: Degradation Model, Algebraic Approach to Restoration, Inverse Filtering, Least Mean Square Filters, Constrained Least Squares Restoration. UNIT IV Image segmentation: Detection of discontinuities. Edge linking and boundary detection, Thresholding, Region oriented segmentation Morphological Image Processing : Dilation and Erosion, Dilation, Structuring Element Decomposition, Erosion, Combining Dilation and Erosion, Opening and Closing, The Hit or Miss Transformation.
UNIT-I
DIGITAL IMAGE FUNDAMENTALS & IMAGE TRANSFORMS
DIGITAL IMAGE FUNDAMENTALS:
The field of digital image processing refers to processing digital images by means of digital computer. Digital image is composed of a finite number of elements, each of which has a particular location and value. These elements are called picture elements, image elements, pels and pixels. Pixel is the term used most widely to denote the elements of digital image. An image is a two-dimensional function that represents a measure of some characteristic such as brightness or color of a viewed scene. An image is a projection of a 3-D scene into a 2D projection plane. An image may be defined as a two-dimensional function f(x,y), where x and y are spatial (plane) coordinates, and the amplitude of f at any pair of coordinates (x,y) is called the intensity of the image at that point. The term gray level is used often to refer to the intensity of monochrome images. Color images are formed by a combination of individual 2-D images. For example: The RGB color system, a color image consists of three (red, green and blue) individual component images. For this reason many of the techniques developed for
monochrome images can be extended to color images by processing the three component images individually. An image may be continuous with respect to the x- and y- coordinates and also in amplitude. Converting such an image to digital form requires that the coordinates, as well as the amplitude, be digitized. APPLICATIONS OF DIGITAL IMAGE PROCESSING Since digital image processing has very wide applications and almost all of the technical fields are impacted by DIP, we will just discuss some of the major applications of DIP. Digital image processing has a broad spectrum of applications, such as Remote sensing via satellites and other spacecrafts Image transmission and storage for business applications Medical processing, RADAR (Radio Detection and Ranging) SONAR(Sound Navigation and Ranging) and Acoustic image processing (The study of underwater sound is known as underwater acoustics or hydro acoustics.) Robotics and automated inspection of industrial parts. Images acquired by satellites are useful in tracking of Earth resources; Geographical mapping; Prediction of agricultural crops, Urban growth and weather monitoring Flood and fire control and many other environmental applications. Space image applications include: Recognition and analysis of objects contained in images obtained from deep space-probe missions. Image transmission and storage applications occur in broadcast television Teleconferencing Transmission of facsimile images(Printed documents and graphics) for office automation
Image Sensors: With reference to sensing, two elements are required to acquire digital image. The first is a physical device that is sensitive to the energy radiated by the object we wish to image and second is specialized image processing hardware. Specialize image processing hardware: It consists of the digitizer just mentioned, plus hardware that performs other primitive operations such as an arithmetic logic unit, which performs arithmetic such addition and subtraction and logical operations in parallel on images. Computer: It is a general purpose computer and can range from a PC to a supercomputer depending on the application. In dedicated applications, sometimes specially designed computer are used to achieve a required level of performance Software: It consists of specialized modules that perform specific tasks a well designed package also includes capability for the user to write code, as a minimum, utilizes the specialized module. More sophisticated software packages allow the integration of these modules. Mass storage: This capability is a must in image processing applications. An image of size 1024 x1024 pixels, in which the intensity of each pixel is an 8- bit quantity requires one Megabytes of storage space if the image is not compressed .Image processing applications falls into three principal categories of storage i) Short term storage for use during processing ii) On line storage for relatively fast retrieval iii) Archival storage such as magnetic tapes and disks Image display: Image displays in use today are mainly color TV monitors. These monitors are driven by the outputs of image and graphics displays cards that are an integral part of computer system. Hardcopy devices: The devices for recording image includes laser printers, film cameras, heat sensitive devices inkjet units and digital units such as optical and CD ROM disk. Films provide the highest possible resolution, but paper is the obvious medium of choice for written applications. Networking: It is almost a default function in any computer system in use today because of the large amount of data inherent in image processing applications. The key consideration in image transmission bandwidth. Fundamental Steps in Digital Image Processing: There are two categories of the steps involved in the image processing –
- Methods whose outputs are input are images.
- Methods whose outputs are attributes extracted from those images. Fig: Fundamental Steps in Digital Image Processing Image acquisition: It could be as simple as being given an image that is already in digital form. Generally the image acquisition stage involves processing such scaling. Image Enhancement: It is among the simplest and most appealing areas of digital image processing. The idea behind this is to bring out details that are obscured or simply to highlight certain features of interest in image. Image enhancement is a very subjective area of image processing. Image Restoration: It deals with improving the appearance of an image. It is an objective approach, in the sense that restoration techniques tend to be based on mathematical or probabilistic models of image processing. Enhancement, on the other hand is based on human subjective preferences regarding what constitutes a “good” enhancement result.
determined by the source of the image. When an image is generated by a physical process, its values are proportional to energy radiated by a physical source. As a consequence, f(x,y) must be nonzero and finite; that is o<f(x,y) <co The function f(x,y) may be characterized by two components- The amount of the source illumination incident on the scene being viewed. (a) The amount of the source illumination reflected back by the objects in the scene These are called illumination and reflectance components and are denoted by i(x,y) an r (x,y) respectively. The functions combine as a product to form f(x,y). We call the intensity of a monochrome image at any coordinates (x,y) the gray level (l) of the image at that point l= f (x, y.) L min ≤ l ≤ Lmax Lmin is to be positive and Lmax must be finite Lmin = imin rmin Lmax = imax rmax The interval [Lmin, Lmax] is called gray scale. Common practice is to shift this interval numerically to the interval [0, L-l] where l=0 is considered black and l= L-1 is considered white on the gray scale. All intermediate values are shades of gray of gray varying from black to white.
SAMPLING AND QUANTIZATION:
To create a digital image, we need to convert the continuous sensed data into digital from. This involves two processes – sampling and quantization. An image may be continuous with respect to the x and y coordinates and also in amplitude. To convert it into digital form we have to sample the function in both coordinates and in amplitudes. Digitalizing the coordinate values is called sampling. Digitalizing the amplitude values is called quantization. There is a continuous the image along the line segment AB. To simple this function, we take equally spaced samples along line AB. The location of each samples is given by a vertical tick back (mark) in the bottom part. The samples are shown as block squares superimposed on function the set of these discrete locations gives the sampled function. In order to form a digital, the gray level values must also be converted (quantized) into discrete quantities. So we divide the gray level scale into eight discrete levels ranging from eight level values. The continuous gray levels are quantized simply by assigning one of the eight discrete gray levels to each sample. The assignment it made depending on the vertical proximity of a simple to a vertical tick mark.
Starting at the top of the image and covering out this procedure line by line produces a two dimensional digital image. Digital Image definition: A digital image f(m,n) described in a 2D discrete space is derived from an analog image f(x,y) in a 2D continuous space through a sampling process that is frequently referred to as digitization. The mathematics of that sampling process will be described in subsequent Chapters. For now we will look at some basic definitions associated with the digital image. The effect of digitization is shown in figure. The 2D continuous image f(x,y) is divided into N rows and M columns. The intersection of a row and a column is termed a pixel. The value assigned to the integer coordinates (m,n) with m=0,1,2..N-1 and n=0,1,2…N-1 is f(m,n). In fact, in most cases, is actually a function of many variables including depth, color and time (t). There are three types of computerized processes in the processing of image
- Low level process - these involve primitive operations such as image processing to reduce noise, contrast enhancement and image sharpening. These kind of processes are characterized by fact the both inputs and output are images.
- Mid level image processing - it involves tasks like segmentation, description of those objects to reduce them to a form suitable for computer processing, and classification of individual objects. The inputs to the process are generally images but outputs are attributes extracted from images. 3) High level processing – It involves “making sense” of an ensemble of recognized objects, as in image analysis, and performing the cognitive functions normally associated with vision. Representing Digital Images: The result of sampling and quantization is matrix of real numbers. Assume that an image f(x,y) is sampled so that the resulting digital image has M rows and N Columns. The values of
Gray levels resolution refers to smallest discernible change in gray levels. Measuring discernible change in gray levels is a highly subjective process reducing the number of bits R while repairing the spatial resolution constant creates the problem of false contouring. It is caused by the use of an insufficient number of gray levels on the smooth areas of the digital image. It is called so because the rides resemble top graphics contours in a map. It is generally quite visible in image displayed using 16 or less uniformly spaced gray levels. Image sensing and Acquisition: The types of images in which we are interested are generated by the combination of an “illumination” source and the reflection or absorption of energy from that source by the elements of the “scene” being imaged. We enclose illumination and scene in quotes to emphasize the fact that they are considerably more general than the familiar situation in which a visible light source illuminates a common everyday 3-D (three-dimensional) scene. For example, the illumination may originate from a source of electromagnetic energy such as radar, infrared, or X-ray energy. But, as noted earlier, it could originate from less traditional sources, such as ultrasound or even a computer-generated illumination pattern. Similarly, the scene elements could be familiar objects, but they can just as easily be molecules, buried rock formations, or a human brain. We could even image a source, such as acquiring images of the sun. Depending on the nature of the source, illumination energy is reflected from, or transmitted through, objects. An example in the first category is light reflected from a planar surface. An example in the second category is when X- rays pass through a patient’s body for the purpose of generating a diagnostic X-ray film. In some applications, the reflected or transmitted energy is focused onto a photo converter (e.g., a phosphor screen), which converts the energy into visible light. Electron microscopy and some applications of gamma imaging use this approach. The idea is simple: Incoming energy is transformed into a voltage by the combination of input electrical power and sensor material that is responsive to the particular type of energy being detected. The output voltage waveform is the response of the sensor(s), and a digital quantity is obtained from each sensor by digitizing its response. In this section, we look at the principal modalities for image sensing and generation.
Fig:Single Image sensor Fig: Line Sensor Fig: Array sensor Image Acquisition using a Single sensor: The components of a single sensor. Perhaps the most familiar sensor of this type is the photodiode, which is constructed of silicon materials and whose output voltage waveform is proportional to light. The use of a filter in front of a sensor improves selectivity. For example, a green (pass) filter in front of a light sensor favors light in the green band of the color spectrum. As a consequence, the sensor output will be stronger for green light than for other components in the visible spectrum.
Fig: Image Acquisition using linear strip and circular strips. Image Acquisition using a Sensor Arrays: The individual sensors arranged in the form of a 2 - D array. Numerous electromagnetic and some ultrasonic sensing devices frequently are arranged in an array format. This is also the predominant arrangement found in digital cameras. A typical sensor for these cameras is a CCD array, which can be manufactured with a broad range of sensing properties and can be packaged in rugged arrays of elements or more. CCD sensors are used widely in digital cameras and other light sensing instruments. The response of each sensor is proportional to the integral of the light energy projected onto the surface of the sensor, a property that is used in astronomical and other applications requiring low noise images. Noise reduction is achieved by letting the sensor integrate the input light signal over minutes or even hours. The two dimensional, its key advantage is that a complete image can be obtained by focusing the energy pattern onto the surface of the array. Motion obviously is not necessary, as is the case with the sensor arrangements This figure shows the energy from an illumination source being reflected from a scene element, but, as mentioned at the beginning of this section, the energy also could be transmitted through the scene elements. The first function performed by the imaging system is to collect the incoming energy and focus it onto an image plane. If the illumination is light, the front end of the imaging system is a lens, which projects the viewed scene onto the lens focal plane. The sensor array, which is coincident with the focal plane, produces outputs proportional
to the integral of the light received at each sensor. Digital and analog circuitry sweep these outputs and convert them to a video signal, which is then digitized by another section of the imaging system. Image sampling and Quantization: To create a digital image, we need to convert the continuous sensed data into digital form. This involves two processes: sampling and quantization. A continuous image, f(x, y), that we want to convert to digital form. An image may be continuous with respect to the x- and y-coordinates, and also in amplitude. To convert it to digital form, we have to sample the function in both coordinates and in amplitude. Digitizing the coordinate values is called sampling. Digitizing the amplitude values is called quantization.
This set of pixels, called the 4- neighbors or p , is denoted by N 4 ( p ). Each pixel is one unit distance from (x,y) and some of the neighbors of p lie outside the digital image if (x,y) is on the border of the image. The four diagonal neighbors of p have coordinates and are denoted by ND ( p ). (x+1, y+1), (x+1, y-1), (x-1, y+1), (x-1, y-1) These points, together with the 4-neighbors, are called the 8-neighbors of p, denoted by N 8 ( p ). As before, some of the points in ND ( p ) and N 8 ( p ) fall outside the image if (x,y) is on the border of the image. ADJACENCY AND CONNECTIVITY Let v be the set of gray – level values used to define adjacency, in a binary image, v={1}. In a gray-scale image, the idea is the same, but V typically contains more elements, for example, V = {180, 181, 182, …, 200}. If the possible intensity values 0 – 255, V set can be any subset of these 256 values. if we are reference to adjacency of pixel with value. Three types of adjacency 4 - Adjacency – two pixel P and Q with value from V are 4 – adjacency if A is in the set N 4 (P)
8 - Adjacency – two pixel P and Q with value from V are 8 – adjacency if A is in the set N 8 (P) M-adjacency^ – two pixel P and Q with value from V are m^ –^ adjacency^ if^ (i) Q^ is in^ N 4 (p) or (ii) Q is in ND(q) and the set N 4 (p) ∩ N 4 (q) has no pixel whose values are from V.
- Mixed adjacency is a modification of 8 - adjacency. It is introduced to eliminate the ambiguities that often arise when 8-adjacency is used.
- For example: Fig:1.8(a) Arrangement of pixels; (b) pixels that are 8-adjacent (shown dashed) to the center pixel; (c) m - adjacency. Types of Adjacency:
- In this example, we can note that to connect between two pixels (finding a path between two pixels):
- In 8-adjacency way, you can find multiple paths between two pixels
- While, in m-adjacency, you can find only one path between two pixels
- So, m-adjacency has eliminated the multiple path connection that has been generated by the 8-adjacency.
- Two subsets^ S 1 and^ S 2 are adjacent,^ if^ some pixel^ in^ S 1 is^ adjacent to^ some^ pixel^ in^ S 2. Adjacent means, either 4-, 8 - or m-adjacency. A Digital Path:
- A digital path (or curve) from pixel p with coordinate ( x , y ) to pixel q with coordinate ( s , t ) is a sequence of distinct pixels with coordinates ( x 0 , y 0 ), ( x 1 , y 1 ), …, ( x n, y n) where ( x 0 , y 0 ) = ( x , y ) and ( x n, y n) = ( s , t ) and pixels ( xi , yi ) and ( xi- 1 , yi- 1 ) are adjacent for 1 ≤ i ≤ n
- n is the length of the path
- If ( x 0 , y 0 ) = ( x n,^ y n), the path^ is^ closed. We can specify 4-, 8- or m-paths depending on the type of adjacency specified.
- Return to the previous example:
