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Digital Image Processing Unit 1 NotesPPT

The document provides an introduction to digital image processing, explaining concepts such as image representation, sampling, quantization, and key stages in processing. It covers various types of digital images, techniques used for image enhancement, restoration, and segmentation, and highlights applications in fields like biometrics and autonomous vehicles. Additionally, it discusses essential relationships between pixels and mathematical operations pertaining to image processing.

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Introduction to Digital Image Processing deepas1@srmist.edu.in Dr.S.Deepa Assistant Professor SRM Institute of Science and Technology
Outline ►Definition ►Image Sampling and Quantization ► Types of Digital Images ►Stages in Digital Image processing ►Applications 2
Digital Image ► A digital image is a representation of a two-dimensional image as a finite set of digital values, called picture elements or pixels. ► Pixel values typically represent gray levels, colours , heights, opacities etc. ► Digitization implies that a digital image is an approximation of a real scene. ► Common image formats include black and white images, grayscale images and RGB images. 3
Digital Image Processing ►Digital Image Processing means processing digital image by means of a digital computer. ►It uses computer algorithms, in order to get enhanced image to extract some useful information. 4
5 Image Acquisition Process
6 Introduction ► What is Digital Image Processing? Digital Image — a two-dimensional function x and y are spatial coordinates The amplitude of f is called intensity or gray level at the point (x, y) Digital Image Processing — process digital images by means of computer, it covers low-, mid-, and high-level processes low-level: inputs and outputs are images mid-level: outputs are attributes extracted from input images high-level: an ensemble of recognition of individual objects Pixel — the elements of a digital image ( , ) f x y
7 A Simple Image Formation Model ( , ) ( , ) ( , ) ( , ): intensity at the point ( , ) ( , ): illumination at the point ( , ) (the amount of source illumination incident on the scene) ( , ): reflectance/transmissivity f x y i x y r x y f x y x y i x y x y r x y   at the point ( , ) (the amount of illumination reflected/transmitted by the object) where 0 < ( , ) < and 0 < ( , ) < 1 x y i x y r x y 
8 Some Typical Ranges of Reflectance ► Reflectance  0.01 for black velvet  0.65 for stainless steel  0.80 for flat-white wall paint  0.90 for silver-plated metal  0.93 for snow
9 Image Sampling and Quantization ► The sampling rate determines the spatial resolution of the digitized image, while the quantization level determines the number of grey levels in the digitized image. ► Hence in order to create an image which is digital, we need to covert continuous data into digital form. There are two steps in which it is done: Sampling Quantization
Image Sampling and Quantization 10 Digitizing the coordinate values Digitizing the amplitude values
11 Image Sampling and Quantization
12 Representing Digital Images ►The representation of an M×N numerical array as (0,0) (0,1) ... (0, 1) (1,0) (1,1) ... (1, 1) ( , ) ... ... ... ... ( 1,0) ( 1,1) ... ( 1, 1) f f f N f f f N f x y f M f M f M N                   
13 Representing Digital Images ►The representation of an M×N numerical array as 0,0 0,1 0, 1 1,0 1,1 1, 1 1,0 1,1 1, 1 ... ... ... ... ... ... ... N N M M M N a a a a a a A a a a                   
14 Representing Digital Images ►The representation of an M×N numerical array in MATLAB (1,1) (1,2) ... (1, ) (2,1) (2,2) ... (2, ) ( , ) ... ... ... ... ( ,1) ( ,2) ... ( , ) f f f N f f f N f x y f M f M f M N             
Types of Digital Images ► Intensity image or monochrome image: Each pixel corresponds to light intensity normally represented in gray scale. ► Color image or RGB image: Each pixel contains a vector representing red, green and blue components. ► Binary image or black and white image: Each pixel contains one bit, 1 represents white and 0 represents black. 15
Image Resolution ► Resolution refers to the number of pixels in an image. The amount of resolution required depends on the amount of details we are interested in. We will now take a look at Image and Intensity Resolution of a digital image. ► Spatial resolution: It is a measure of the smallest discernible detail in an image. Vision specialists state it with dots (pixels) per unit distance, graphic designers state it with dots per inch (dpi). ► Intensity Level Resolution: It refers to the number of intensity levels used to represent the image. The more intensity levels used, the finer the level of detail discernable in an image. Intensity level resolution is usually given in terms of the number of bits used to store each intensity level. 16
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19 Representing Digital Images ► Discrete intensity interval [0, L-1], L=2k ► The number b of bits required to store a M × N digitized image b = M × N × k
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Key Stages in Digital Image Processing Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression 23
Key Stages in Digital Image Processing: Image Aquisition Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression 24
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Key Stages in Digital Image Processing: Image Enhancement Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression Images taken from Gonzalez & Woods, Digital Image Processing (2002) 26
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►Image enhancement is the procedure of improving the quality and information content of original data before processing. ►For example, you can remove noise, sharpen, or brighten an image, making it easier to identify key features. 28
Here are some useful examples and methods of image enhancement: ► Filtering with morphological operators ► Histogram equalization ► Noise removal using a Wiener filter ► Linear contrast adjustment ► Median filtering ► Unsharp mask filtering ► Contrast-limited adaptive histogram equalization (CLAHE) ► Decorrelation stretch 29
Correcting nonuniform illumination with morphological operators. 30 Enhancing grayscale images with histogram equalization.
Key Stages in Digital Image Processing: Image Restoration Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression Images taken from Gonzalez & Woods, Digital Image Processing (2002) 31
Image Restoration ►To restore extremely blurred or degraded image. Images blurred due to many factors like relative motion between camera and a moving car (eg. Image of a speeding car). ►Inverse filter, Wiener filter & Lucy- Richardson filters are used to restore images. 32
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Key Stages in Digital Image Processing: Morphological Processing Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression Images taken from Gonzalez & Woods, Digital Image Processing (2002) 34
► Morphology is a broad set of image processing operations that process images based on shapes. Morphological operations apply a structuring element to an input image, creating an output image of the same size. ► The most basic morphological operations are dilation and erosion. Dilation adds pixels to the boundaries of objects in an image, while erosion removes pixels on object boundaries. 35
Dilation 36 Erosion
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Key Stages in Digital Image Processing: Segmentation Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression Images taken from Gonzalez & Woods, Digital Image Processing (2002) 38
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Types of Segmentation ►Thresholding Segmentation. ►Edge-Based Segmentation. ►Region-Based Segmentation. ►Watershed Segmentation. ►Clustering- Based Segmentation Algorithms. ►Neural Networks for Segmentation. https://www.mathworks.com/discovery/ image-segmentation.html 40
Key Stages in Digital Image Processing: Object Recognition Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression Images taken from Gonzalez & Woods, Digital Image Processing (2002) 41
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►https://www.mathworks.com/solutions/ image-video-processing/object- recognition.html 43
Key Stages in Digital Image Processing: Representation & Description Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression Images taken from Gonzalez & Woods, Digital Image Processing (2002) 44
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Key Stages in Digital Image Processing: Image Compression Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression 47
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Key Stages in Digital Image Processing: Colour Image Processing Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression 49
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Applications & Research Topics 56
57 Document Handling
Signature Verification 58
Biometrics 59
Fingerprint Verification / Identification 60
Object Recognition 61
Object Recognition Research reference view 1 reference view 2 novel view recognized 62
Indexing into Databases ►Shape content 63
64 Indexing into Databases (cont’d) ►Color, texture
Target Recognition ►Department of Defense (Army, Airforce, Navy) 65
Interpretation of aerial photography is a problem domain in both computer vision and registration. Interpretation of Aerial Photography 66
Autonomous Vehicles ►Land, Underwater, Space 67
Traffic Monitoring 68
Face Detection 69
Face Recognition 70
Facial Expression Recognition 71
72 Hand Gesture Recognition ► Smart Human-Computer User Interfaces ► Sign Language Recognition
Human Activity Recognition 73
Medical Applications ► skin cancer breast cancer 74
Morphing 75
Inserting Artificial Objects into a Scene 76
Companies In this Field In India ► Sarnoff Corporation ► Kritikal Solutions ► National Instruments ► GE Laboratories ► Ittiam, Bangalore ► Interra Systems, Noida ► Yahoo India (Multimedia Searching) ► nVidia Graphics, Pune (have high requirements) ► Microsoft research ► DRDO labs ► ISRO labs ► … 77
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Neighborhood Operations in Images 79
80 Basic Relationships Between Pixels ► Neighborhood ► Adjacency ► Connectivity ► Paths ► Regions and boundaries
81 Basic Relationships Between Pixels ► Neighbors of a pixel p at coordinates (x,y)  4-neighbors of p, denoted by N4(p): (x-1, y), (x+1, y), (x,y-1), and (x, y+1).  4 diagonal neighbors of p, denoted by ND(p): (x-1, y-1), (x+1, y+1), (x+1,y-1), and (x-1, y+1).  8 neighbors of p, denoted N8(p) N8(p) = N4(p) U ND(p)
82 Basic Relationships Between Pixels ► Adjacency Let V be the set of intensity values  4-adjacency: Two pixels p and q with values from V are 4-adjacent if q is in the set N4(p).  8-adjacency: Two pixels p and q with values from V are 8-adjacent if q is in the set N8(p).
83 Basic Relationships Between Pixels ► Adjacency Let V be the set of intensity values  m-adjacency: Two pixels p and q with values from V are m-adjacent if (i) q is in the set N4(p), or (ii) q is in the set ND(p) and the set N4(p) ∩ N4(p) has no pixels whose values are from V.
84 Basic Relationships Between Pixels ► Path  A (digital) path (or curve) from pixel p with coordinates (x0, y0) to pixel q with coordinates (xn, yn) is a sequence of distinct pixels with coordinates (x0, y0), (x1, y1), …, (xn, yn) Where (xi, yi) and (xi-1, yi-1) are adjacent for 1 i n. ≤ ≤  Here n is the length of the path.  If (x0, y0) = (xn, yn), the path is closed path.  We can define 4-, 8-, and m-paths based on the type of adjacency used.
85 Examples: Adjacency and Path 0 1 1 0 1 1 0 1 1 0 2 0 0 2 0 0 2 0 0 0 1 0 0 1 0 0 1 V = {1, 2}
86 Examples: Adjacency and Path 0 1 1 0 1 1 0 1 1 0 2 0 0 2 0 0 2 0 0 0 1 0 0 1 0 0 1 V = {1, 2} 8-adjacent
87 Examples: Adjacency and Path 0 1 1 0 1 1 0 1 1 0 2 0 0 2 0 0 2 0 0 0 1 0 0 1 0 0 1 V = {1, 2} 8-adjacent m-adjacent
88 Examples: Adjacency and Path 01,1 11,2 11,3 0 1 1 0 1 1 02,1 22,2 02,3 0 2 0 0 2 0 03,1 03,2 13,3 0 0 1 0 0 1 V = {1, 2} 8-adjacent m-adjacent The 8-path from (1,3) to (3,3): (i) (1,3), (1,2), (2,2), (3,3) (ii) (1,3), (2,2), (3,3) The m-path from (1,3) to (3,3): (1,3), (1,2), (2,2), (3,3)
89 Basic Relationships Between Pixels ► Connected in S Let S represent a subset of pixels in an image. Two pixels p with coordinates (x0, y0) and q with coordinates (xn, yn) are said to be connected in S if there exists a path (x0, y0), (x1, y1), …, (xn, yn) Where ,0 ,( , ) i i i i n x y S    
90 Basic Relationships Between Pixels Let S represent a subset of pixels in an image ► For every pixel p in S, the set of pixels in S that are connected to p is called a connected component of S. ► If S has only one connected component, then S is called Connected Set. ► We call R a region of the image if R is a connected set ► Two regions, Ri and Rj are said to be adjacent if their union forms a connected set. ► Regions that are not to be adjacent are said to be disjoint.
91 Basic Relationships Between Pixels ► Boundary (or border)  The boundary of the region R is the set of pixels in the region that have one or more neighbors that are not in R.  If R happens to be an entire image, then its boundary is defined as the set of pixels in the first and last rows and columns of the image. ► Foreground and background  An image contains K disjoint regions, Rk, k = 1, 2, …, K. Let Ru denote the union of all the K regions, and let (Ru)c denote its complement. All the points in Ru is called foreground; All the points in (Ru)c is called background.
92 Distance Measures ► Given pixels p, q and z with coordinates (x, y), (s, t), (u, v) respectively, the distance function D has following properties: a. D(p, q) 0 [D(p, q) = 0, iff p = q] ≥ b. D(p, q) = D(q, p) c. D(p, z) D(p, q) + D(q, z) ≤
93 Distance Measures The following are the different Distance measures: a. Euclidean Distance : De(p, q) = [(x-s)2 + (y-t)2 ]1/2 b. City Block Distance: D4(p, q) = |x-s| + |y-t| c. Chess Board Distance: D8(p, q) = max(|x-s|, |y-t|)
94 Introduction to Mathematical Operations in DIP ► Array vs. Matrix Operation 11 12 21 22 b b B b b       11 12 21 22 a a A a a       11 11 12 21 11 12 12 22 21 11 22 21 21 12 22 22 * a b a b a b a b A B a b a b a b a b           11 11 12 12 21 21 22 22 .* a b a b A B a b a b       Array product Matrix product Array product operator Matrix product operator
95 Arithmetic Operations ► Arithmetic operations between images are array operations. The four arithmetic operations are denoted as s(x,y) = f(x,y) + g(x,y) d(x,y) = f(x,y) – g(x,y) p(x,y) = f(x,y) × g(x,y) v(x,y) = f(x,y) ÷ g(x,y)
96 Example: Addition of Noisy Images for Noise Reduction Noiseless image: f(x,y) Noise: n(x,y) (at every pair of coordinates (x,y), the noise is uncorrelated and has zero average value) Corrupted image: g(x,y) g(x,y) = f(x,y) + n(x,y) Reducing the noise by adding a set of noisy images, {gi(x,y)} 1 1 ( , ) ( , ) K i i g x y g x y K   
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98 An Example of Image Subtraction: Mask Mode Radiography Mask h(x,y): an X-ray image of a region of a patient’s body Live images f(x,y): X-ray images captured at TV rates after injection of the contrast medium Enhanced detail g(x,y) g(x,y) = f(x,y) - h(x,y) The procedure gives a movie showing how the contrast medium propagates through the various arteries in the area being observed.
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100 An Example of Image Multiplication
101 Set and Logical Operations
102 Set and Logical Operations ► Let A be the elements of a gray-scale image The elements of A are triplets of the form (x, y, z), where x and y are spatial coordinates and z denotes the intensity at the point (x, y). ► The complement of A is denoted Ac {( , , ) | ( , , ) } 2 1; is the number of intensity bits used to represent c k A x y K z x y z A K k z      {( , , ) | ( , )} A x y z z f x y  
103 Set and Logical Operations ► The union of two gray-scale images (sets) A and B is defined as the set {max( , ) | , } z A B a b a A b B    
104 Set and Logical Operations
105 Set and Logical Operations
106 Spatial Operations ► Single-pixel operations Alter the values of an image’s pixels based on the intensity. e.g., ( ) s T z 
107 Spatial Operations ► Neighborhood operations The value of this pixel is determined by a specified operation involving the pixels in the input image with coordinates in Sxy
108 Spatial Operations ► Neighborhood operations
109 Geometric Spatial Transformations ► Geometric transformation (rubber-sheet transformation) — A spatial transformation of coordinates — intensity interpolation that assigns intensity values to the spatially transformed pixels. ► Affine transform ( , ) {( , )} x y T v w      11 12 21 22 31 32 0 1 1 0 1 t t x y v w t t t t           
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111 Image Registration ► Input and output images are available but the transformation function is unknown. Goal: estimate the transformation function and use it to register the two images. ► One of the principal approaches for image registration is to use tie points (also called control points)  The corresponding points are known precisely in the input and output (reference) images.
112 Image Registration ► A simple model based on bilinear approximation: 1 2 3 4 5 6 7 8 Where ( , ) and ( , ) are the coordinates of tie points in the input and reference images. x c v c w c vw c y c v c w c vw c v w x y           
113 Image Registration
114 Image Transform ► A particularly important class of 2-D linear transforms, denoted T(u, v) 1 1 0 0 ( , ) ( , ) ( , , , ) where ( , ) is the input image, ( , , , ) is the ker , variables and are the transform variables, = 0, 1, 2, ..., M-1 and = 0, 1, M N x y T u v f x y r x y u v f x y r x y u v forward transformation nel u v u v      ..., N-1.
115 Image Transform ► Given T(u, v), the original image f(x, y) can be recoverd using the inverse tranformation of T(u, v). 1 1 0 0 ( , ) ( , ) ( , , , ) where ( , , , ) is the ker , = 0, 1, 2, ..., M-1 and = 0, 1, ..., N-1. M N u v f x y T u v s x y u v s x y u v inverse transformation nel x y     
116 Image Transform
117 Example: Image Denoising by Using DCT Transform
118 Forward Transform Kernel 1 1 0 0 1 2 1 2 ( , ) ( , ) ( , , , ) The kernel ( , , , ) is said to be SEPERABLE if ( , , , ) ( , ) ( , ) In addition, the kernel is said to be SYMMETRIC if ( , ) is functionally equal to ( , M N x y T u v f x y r x y u v r x y u v r x y u v r x u r y v r x u r y v        1 1 ), so that ( , , , ) ( , ) ( , ) r x y u v r x u r y u 
119 The Kernels for 2-D Fourier Transform 2 ( / / ) 2 ( / / ) The kernel ( , , , ) Where = 1 The kernel 1 ( , , , ) j ux M vy N j ux M vy N forward r x y u v e j inverse s x y u v e MN        
120 2-D Fourier Transform 1 1 2 ( / / ) 0 0 1 1 2 ( / / ) 0 0 ( , ) ( , ) 1 ( , ) ( , ) M N j ux M vy N x y M N j ux M vy N u v T u v f x y e f x y T u v e MN                 
121 Probabilistic Methods Let , 0, 1, 2, ..., -1, denote the values of all possible intensities in an digital image. The probability, ( ), of intensity level occurring in a given image is estimated as i k k z i L M N p z z   ( ) , where is the number of times that intensity occurs in the image. k k k k n p z MN n z  1 0 ( ) 1 L k k p z     1 0 The mean (average) intensity is given by = ( ) L k k k m z p z   
122 Probabilistic Methods 1 2 2 0 The variance of the intensities is given by = ( ) ( ) L k k k z m p z      th 1 0 The moment of the intensity variable is ( ) = ( ) ( ) L n n k k k n z u z z m p z    
123 Example: Comparison of Standard Deviation Values 31.6   14.3   49.2  

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Digital Image Processing Unit 1 NotesPPT

  • 1.
    Introduction to DigitalImage Processing deepas1@srmist.edu.in Dr.S.Deepa Assistant Professor SRM Institute of Science and Technology
  • 2.
    Outline ►Definition ►Image Sampling andQuantization ► Types of Digital Images ►Stages in Digital Image processing ►Applications 2
  • 3.
    Digital Image ► Adigital image is a representation of a two-dimensional image as a finite set of digital values, called picture elements or pixels. ► Pixel values typically represent gray levels, colours , heights, opacities etc. ► Digitization implies that a digital image is an approximation of a real scene. ► Common image formats include black and white images, grayscale images and RGB images. 3
  • 4.
    Digital Image Processing ►DigitalImage Processing means processing digital image by means of a digital computer. ►It uses computer algorithms, in order to get enhanced image to extract some useful information. 4
  • 5.
  • 6.
    6 Introduction ► What isDigital Image Processing? Digital Image — a two-dimensional function x and y are spatial coordinates The amplitude of f is called intensity or gray level at the point (x, y) Digital Image Processing — process digital images by means of computer, it covers low-, mid-, and high-level processes low-level: inputs and outputs are images mid-level: outputs are attributes extracted from input images high-level: an ensemble of recognition of individual objects Pixel — the elements of a digital image ( , ) f x y
  • 7.
    7 A Simple ImageFormation Model ( , ) ( , ) ( , ) ( , ): intensity at the point ( , ) ( , ): illumination at the point ( , ) (the amount of source illumination incident on the scene) ( , ): reflectance/transmissivity f x y i x y r x y f x y x y i x y x y r x y   at the point ( , ) (the amount of illumination reflected/transmitted by the object) where 0 < ( , ) < and 0 < ( , ) < 1 x y i x y r x y 
  • 8.
    8 Some Typical Rangesof Reflectance ► Reflectance  0.01 for black velvet  0.65 for stainless steel  0.80 for flat-white wall paint  0.90 for silver-plated metal  0.93 for snow
  • 9.
    9 Image Sampling andQuantization ► The sampling rate determines the spatial resolution of the digitized image, while the quantization level determines the number of grey levels in the digitized image. ► Hence in order to create an image which is digital, we need to covert continuous data into digital form. There are two steps in which it is done: Sampling Quantization
  • 10.
    Image Sampling and Quantization 10 Digitizingthe coordinate values Digitizing the amplitude values
  • 11.
  • 12.
    12 Representing Digital Images ►Therepresentation of an M×N numerical array as (0,0) (0,1) ... (0, 1) (1,0) (1,1) ... (1, 1) ( , ) ... ... ... ... ( 1,0) ( 1,1) ... ( 1, 1) f f f N f f f N f x y f M f M f M N                   
  • 13.
    13 Representing Digital Images ►Therepresentation of an M×N numerical array as 0,0 0,1 0, 1 1,0 1,1 1, 1 1,0 1,1 1, 1 ... ... ... ... ... ... ... N N M M M N a a a a a a A a a a                   
  • 14.
    14 Representing Digital Images ►Therepresentation of an M×N numerical array in MATLAB (1,1) (1,2) ... (1, ) (2,1) (2,2) ... (2, ) ( , ) ... ... ... ... ( ,1) ( ,2) ... ( , ) f f f N f f f N f x y f M f M f M N             
  • 15.
    Types of DigitalImages ► Intensity image or monochrome image: Each pixel corresponds to light intensity normally represented in gray scale. ► Color image or RGB image: Each pixel contains a vector representing red, green and blue components. ► Binary image or black and white image: Each pixel contains one bit, 1 represents white and 0 represents black. 15
  • 16.
    Image Resolution ► Resolutionrefers to the number of pixels in an image. The amount of resolution required depends on the amount of details we are interested in. We will now take a look at Image and Intensity Resolution of a digital image. ► Spatial resolution: It is a measure of the smallest discernible detail in an image. Vision specialists state it with dots (pixels) per unit distance, graphic designers state it with dots per inch (dpi). ► Intensity Level Resolution: It refers to the number of intensity levels used to represent the image. The more intensity levels used, the finer the level of detail discernable in an image. Intensity level resolution is usually given in terms of the number of bits used to store each intensity level. 16
  • 17.
  • 18.
  • 19.
    19 Representing Digital Images ►Discrete intensity interval [0, L-1], L=2k ► The number b of bits required to store a M × N digitized image b = M × N × k
  • 20.
  • 21.
  • 22.
  • 23.
    Key Stages inDigital Image Processing Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression 23
  • 24.
    Key Stages inDigital Image Processing: Image Aquisition Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression 24
  • 25.
  • 26.
    Key Stages inDigital Image Processing: Image Enhancement Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression Images taken from Gonzalez & Woods, Digital Image Processing (2002) 26
  • 27.
  • 28.
    ►Image enhancement isthe procedure of improving the quality and information content of original data before processing. ►For example, you can remove noise, sharpen, or brighten an image, making it easier to identify key features. 28
  • 29.
    Here are someuseful examples and methods of image enhancement: ► Filtering with morphological operators ► Histogram equalization ► Noise removal using a Wiener filter ► Linear contrast adjustment ► Median filtering ► Unsharp mask filtering ► Contrast-limited adaptive histogram equalization (CLAHE) ► Decorrelation stretch 29
  • 30.
    Correcting nonuniform illuminationwith morphological operators. 30 Enhancing grayscale images with histogram equalization.
  • 31.
    Key Stages inDigital Image Processing: Image Restoration Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression Images taken from Gonzalez & Woods, Digital Image Processing (2002) 31
  • 32.
    Image Restoration ►To restoreextremely blurred or degraded image. Images blurred due to many factors like relative motion between camera and a moving car (eg. Image of a speeding car). ►Inverse filter, Wiener filter & Lucy- Richardson filters are used to restore images. 32
  • 33.
  • 34.
    Key Stages inDigital Image Processing: Morphological Processing Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression Images taken from Gonzalez & Woods, Digital Image Processing (2002) 34
  • 35.
    ► Morphology isa broad set of image processing operations that process images based on shapes. Morphological operations apply a structuring element to an input image, creating an output image of the same size. ► The most basic morphological operations are dilation and erosion. Dilation adds pixels to the boundaries of objects in an image, while erosion removes pixels on object boundaries. 35
  • 36.
  • 37.
  • 38.
    Key Stages inDigital Image Processing: Segmentation Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression Images taken from Gonzalez & Woods, Digital Image Processing (2002) 38
  • 39.
  • 40.
    Types of Segmentation ►ThresholdingSegmentation. ►Edge-Based Segmentation. ►Region-Based Segmentation. ►Watershed Segmentation. ►Clustering- Based Segmentation Algorithms. ►Neural Networks for Segmentation. https://www.mathworks.com/discovery/ image-segmentation.html 40
  • 41.
    Key Stages inDigital Image Processing: Object Recognition Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression Images taken from Gonzalez & Woods, Digital Image Processing (2002) 41
  • 42.
  • 43.
  • 44.
    Key Stages inDigital Image Processing: Representation & Description Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression Images taken from Gonzalez & Woods, Digital Image Processing (2002) 44
  • 45.
  • 46.
  • 47.
    Key Stages inDigital Image Processing: Image Compression Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression 47
  • 48.
  • 49.
    Key Stages inDigital Image Processing: Colour Image Processing Image Acquisition Image Restoration Morphologica l Processing Segmentation Representatio n & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression 49
  • 50.
  • 51.
  • 52.
  • 53.
  • 54.
  • 55.
  • 56.
  • 57.
  • 58.
  • 59.
  • 60.
  • 61.
  • 62.
    Object Recognition Research referenceview 1 reference view 2 novel view recognized 62
  • 63.
  • 64.
  • 65.
    Target Recognition ►Department ofDefense (Army, Airforce, Navy) 65
  • 66.
    Interpretation of aerialphotography is a problem domain in both computer vision and registration. Interpretation of Aerial Photography 66
  • 67.
  • 68.
  • 69.
  • 70.
  • 71.
  • 72.
    72 Hand Gesture Recognition ►Smart Human-Computer User Interfaces ► Sign Language Recognition
  • 73.
  • 74.
    Medical Applications ► skincancer breast cancer 74
  • 75.
  • 76.
  • 77.
    Companies In thisField In India ► Sarnoff Corporation ► Kritikal Solutions ► National Instruments ► GE Laboratories ► Ittiam, Bangalore ► Interra Systems, Noida ► Yahoo India (Multimedia Searching) ► nVidia Graphics, Pune (have high requirements) ► Microsoft research ► DRDO labs ► ISRO labs ► … 77
  • 78.
  • 79.
  • 80.
    80 Basic Relationships BetweenPixels ► Neighborhood ► Adjacency ► Connectivity ► Paths ► Regions and boundaries
  • 81.
    81 Basic Relationships BetweenPixels ► Neighbors of a pixel p at coordinates (x,y)  4-neighbors of p, denoted by N4(p): (x-1, y), (x+1, y), (x,y-1), and (x, y+1).  4 diagonal neighbors of p, denoted by ND(p): (x-1, y-1), (x+1, y+1), (x+1,y-1), and (x-1, y+1).  8 neighbors of p, denoted N8(p) N8(p) = N4(p) U ND(p)
  • 82.
    82 Basic Relationships BetweenPixels ► Adjacency Let V be the set of intensity values  4-adjacency: Two pixels p and q with values from V are 4-adjacent if q is in the set N4(p).  8-adjacency: Two pixels p and q with values from V are 8-adjacent if q is in the set N8(p).
  • 83.
    83 Basic Relationships BetweenPixels ► Adjacency Let V be the set of intensity values  m-adjacency: Two pixels p and q with values from V are m-adjacent if (i) q is in the set N4(p), or (ii) q is in the set ND(p) and the set N4(p) ∩ N4(p) has no pixels whose values are from V.
  • 84.
    84 Basic Relationships BetweenPixels ► Path  A (digital) path (or curve) from pixel p with coordinates (x0, y0) to pixel q with coordinates (xn, yn) is a sequence of distinct pixels with coordinates (x0, y0), (x1, y1), …, (xn, yn) Where (xi, yi) and (xi-1, yi-1) are adjacent for 1 i n. ≤ ≤  Here n is the length of the path.  If (x0, y0) = (xn, yn), the path is closed path.  We can define 4-, 8-, and m-paths based on the type of adjacency used.
  • 85.
    85 Examples: Adjacency andPath 0 1 1 0 1 1 0 1 1 0 2 0 0 2 0 0 2 0 0 0 1 0 0 1 0 0 1 V = {1, 2}
  • 86.
    86 Examples: Adjacency andPath 0 1 1 0 1 1 0 1 1 0 2 0 0 2 0 0 2 0 0 0 1 0 0 1 0 0 1 V = {1, 2} 8-adjacent
  • 87.
    87 Examples: Adjacency andPath 0 1 1 0 1 1 0 1 1 0 2 0 0 2 0 0 2 0 0 0 1 0 0 1 0 0 1 V = {1, 2} 8-adjacent m-adjacent
  • 88.
    88 Examples: Adjacency andPath 01,1 11,2 11,3 0 1 1 0 1 1 02,1 22,2 02,3 0 2 0 0 2 0 03,1 03,2 13,3 0 0 1 0 0 1 V = {1, 2} 8-adjacent m-adjacent The 8-path from (1,3) to (3,3): (i) (1,3), (1,2), (2,2), (3,3) (ii) (1,3), (2,2), (3,3) The m-path from (1,3) to (3,3): (1,3), (1,2), (2,2), (3,3)
  • 89.
    89 Basic Relationships BetweenPixels ► Connected in S Let S represent a subset of pixels in an image. Two pixels p with coordinates (x0, y0) and q with coordinates (xn, yn) are said to be connected in S if there exists a path (x0, y0), (x1, y1), …, (xn, yn) Where ,0 ,( , ) i i i i n x y S    
  • 90.
    90 Basic Relationships BetweenPixels Let S represent a subset of pixels in an image ► For every pixel p in S, the set of pixels in S that are connected to p is called a connected component of S. ► If S has only one connected component, then S is called Connected Set. ► We call R a region of the image if R is a connected set ► Two regions, Ri and Rj are said to be adjacent if their union forms a connected set. ► Regions that are not to be adjacent are said to be disjoint.
  • 91.
    91 Basic Relationships BetweenPixels ► Boundary (or border)  The boundary of the region R is the set of pixels in the region that have one or more neighbors that are not in R.  If R happens to be an entire image, then its boundary is defined as the set of pixels in the first and last rows and columns of the image. ► Foreground and background  An image contains K disjoint regions, Rk, k = 1, 2, …, K. Let Ru denote the union of all the K regions, and let (Ru)c denote its complement. All the points in Ru is called foreground; All the points in (Ru)c is called background.
  • 92.
    92 Distance Measures ► Givenpixels p, q and z with coordinates (x, y), (s, t), (u, v) respectively, the distance function D has following properties: a. D(p, q) 0 [D(p, q) = 0, iff p = q] ≥ b. D(p, q) = D(q, p) c. D(p, z) D(p, q) + D(q, z) ≤
  • 93.
    93 Distance Measures The followingare the different Distance measures: a. Euclidean Distance : De(p, q) = [(x-s)2 + (y-t)2 ]1/2 b. City Block Distance: D4(p, q) = |x-s| + |y-t| c. Chess Board Distance: D8(p, q) = max(|x-s|, |y-t|)
  • 94.
    94 Introduction to MathematicalOperations in DIP ► Array vs. Matrix Operation 11 12 21 22 b b B b b       11 12 21 22 a a A a a       11 11 12 21 11 12 12 22 21 11 22 21 21 12 22 22 * a b a b a b a b A B a b a b a b a b           11 11 12 12 21 21 22 22 .* a b a b A B a b a b       Array product Matrix product Array product operator Matrix product operator
  • 95.
    95 Arithmetic Operations ► Arithmeticoperations between images are array operations. The four arithmetic operations are denoted as s(x,y) = f(x,y) + g(x,y) d(x,y) = f(x,y) – g(x,y) p(x,y) = f(x,y) × g(x,y) v(x,y) = f(x,y) ÷ g(x,y)
  • 96.
    96 Example: Addition ofNoisy Images for Noise Reduction Noiseless image: f(x,y) Noise: n(x,y) (at every pair of coordinates (x,y), the noise is uncorrelated and has zero average value) Corrupted image: g(x,y) g(x,y) = f(x,y) + n(x,y) Reducing the noise by adding a set of noisy images, {gi(x,y)} 1 1 ( , ) ( , ) K i i g x y g x y K   
  • 97.
  • 98.
    98 An Example ofImage Subtraction: Mask Mode Radiography Mask h(x,y): an X-ray image of a region of a patient’s body Live images f(x,y): X-ray images captured at TV rates after injection of the contrast medium Enhanced detail g(x,y) g(x,y) = f(x,y) - h(x,y) The procedure gives a movie showing how the contrast medium propagates through the various arteries in the area being observed.
  • 99.
  • 100.
    100 An Example ofImage Multiplication
  • 101.
  • 102.
    102 Set and LogicalOperations ► Let A be the elements of a gray-scale image The elements of A are triplets of the form (x, y, z), where x and y are spatial coordinates and z denotes the intensity at the point (x, y). ► The complement of A is denoted Ac {( , , ) | ( , , ) } 2 1; is the number of intensity bits used to represent c k A x y K z x y z A K k z      {( , , ) | ( , )} A x y z z f x y  
  • 103.
    103 Set and LogicalOperations ► The union of two gray-scale images (sets) A and B is defined as the set {max( , ) | , } z A B a b a A b B    
  • 104.
  • 105.
  • 106.
    106 Spatial Operations ► Single-pixeloperations Alter the values of an image’s pixels based on the intensity. e.g., ( ) s T z 
  • 107.
    107 Spatial Operations ► Neighborhoodoperations The value of this pixel is determined by a specified operation involving the pixels in the input image with coordinates in Sxy
  • 108.
  • 109.
    109 Geometric Spatial Transformations ►Geometric transformation (rubber-sheet transformation) — A spatial transformation of coordinates — intensity interpolation that assigns intensity values to the spatially transformed pixels. ► Affine transform ( , ) {( , )} x y T v w      11 12 21 22 31 32 0 1 1 0 1 t t x y v w t t t t           
  • 110.
  • 111.
    111 Image Registration ► Inputand output images are available but the transformation function is unknown. Goal: estimate the transformation function and use it to register the two images. ► One of the principal approaches for image registration is to use tie points (also called control points)  The corresponding points are known precisely in the input and output (reference) images.
  • 112.
    112 Image Registration ► Asimple model based on bilinear approximation: 1 2 3 4 5 6 7 8 Where ( , ) and ( , ) are the coordinates of tie points in the input and reference images. x c v c w c vw c y c v c w c vw c v w x y           
  • 113.
  • 114.
    114 Image Transform ► Aparticularly important class of 2-D linear transforms, denoted T(u, v) 1 1 0 0 ( , ) ( , ) ( , , , ) where ( , ) is the input image, ( , , , ) is the ker , variables and are the transform variables, = 0, 1, 2, ..., M-1 and = 0, 1, M N x y T u v f x y r x y u v f x y r x y u v forward transformation nel u v u v      ..., N-1.
  • 115.
    115 Image Transform ► GivenT(u, v), the original image f(x, y) can be recoverd using the inverse tranformation of T(u, v). 1 1 0 0 ( , ) ( , ) ( , , , ) where ( , , , ) is the ker , = 0, 1, 2, ..., M-1 and = 0, 1, ..., N-1. M N u v f x y T u v s x y u v s x y u v inverse transformation nel x y     
  • 116.
  • 117.
    117 Example: Image Denoisingby Using DCT Transform
  • 118.
    118 Forward Transform Kernel 11 0 0 1 2 1 2 ( , ) ( , ) ( , , , ) The kernel ( , , , ) is said to be SEPERABLE if ( , , , ) ( , ) ( , ) In addition, the kernel is said to be SYMMETRIC if ( , ) is functionally equal to ( , M N x y T u v f x y r x y u v r x y u v r x y u v r x u r y v r x u r y v        1 1 ), so that ( , , , ) ( , ) ( , ) r x y u v r x u r y u 
  • 119.
    119 The Kernels for2-D Fourier Transform 2 ( / / ) 2 ( / / ) The kernel ( , , , ) Where = 1 The kernel 1 ( , , , ) j ux M vy N j ux M vy N forward r x y u v e j inverse s x y u v e MN        
  • 120.
    120 2-D Fourier Transform 11 2 ( / / ) 0 0 1 1 2 ( / / ) 0 0 ( , ) ( , ) 1 ( , ) ( , ) M N j ux M vy N x y M N j ux M vy N u v T u v f x y e f x y T u v e MN                 
  • 121.
    121 Probabilistic Methods Let ,0, 1, 2, ..., -1, denote the values of all possible intensities in an digital image. The probability, ( ), of intensity level occurring in a given image is estimated as i k k z i L M N p z z   ( ) , where is the number of times that intensity occurs in the image. k k k k n p z MN n z  1 0 ( ) 1 L k k p z     1 0 The mean (average) intensity is given by = ( ) L k k k m z p z   
  • 122.
    122 Probabilistic Methods 1 2 2 0 Thevariance of the intensities is given by = ( ) ( ) L k k k z m p z      th 1 0 The moment of the intensity variable is ( ) = ( ) ( ) L n n k k k n z u z z m p z    
  • 123.
    123 Example: Comparison ofStandard Deviation Values 31.6   14.3   49.2  

Editor's Notes

  • #20 As opposed to [0..255]