Image Processing (EA C443) OBJECTIVES: To study components of the Image (Digital Image) To Know how the image quality can be improved How efficiently the image data can be stored and transmitted How the image can be reconstructed from the projections To study some of the Applications
Image Formation Model Let us consider an image y Smallest element in this picture is a pixel (Picture element). Collection of these pixels with various intensity levels constitute an image. Picture or an image is considered to be a 2 dimensional Signal or data in the form of matrix. f(x,y) x
Image Formation Model Image data in the form of matrix, which is a 2D function f(x,y) 95 102 94 102 95 98 102 99 103 105 110 94 99 94 101 100 98 100 101 101 107 104 97 86 83 97 96 98 104 96 100 102 102 105 91 85 93 89 98 92 95 98 100 102 106 105 99 90 93 96 84 88 93 89 89 98 94 102 99 81 87 86 84 90 91 88 101 104 87 82 90 84 86 87 86 95 102 99 102 90 74 92 101 87 74 77 83 100 92 95 102 100 92 96 110 93 72 71 83 101 87 103 101 105 88 76 94 93 71 69 105 99 105 104 111 101 84 59 78 102 72
Simple Image acquisition model Light Source Photo detector DIGITIZATION DIGITAL IMAGE
Image Model Image Model Spatial coordinates 0 to f ( x, y) i( x, y) r( x, y) 0 to 1 Incident component Reflected component
DIGITIZATION Analog-to-Digital conversion Digitization = Sampling + Quantization (+ Coding) Sampling digitization of temporal or spatial coordinates Quantization digitization of amplitude or intensity Coding reduce/minimize the amount of data
DIGITIZATION (SAMPLING) Digitizing the coordinates values is called as sampling Pixel at coordinate (x,y) or at m th row and n th column
Image Sampling and Quantization Digitizing the amplitude values is called as quantization
Image Sampling and Quantization Image before sampling and quantization Image after sampling and quantization
Representing Digital Images Digital Image is obtained after sampling and quantization, which is a 2D array f(x,y), which has M rows and N columns. i.e x=0,1,2,3,,m-1 and y=0,1,2,3,.,n-1 x and y are called as spatial coordinates.
Representing Digital Images Matrix Representation f ( x, y) f (0,0) f (1,0) f ( M 1,0) f (0,1) f (1,1) f ( M 1,1) f (0, N 1) f (1, N 1) f ( M 1, N 1) Values in this matrix depends on the intensity levels. Which is decided upon the quantization of the amplitude level. There are L level of quantization is decided based on the dynamic range of an imaging system. L=2 k.
Representing Digital Images These levels are called as gray levels. Which range from 0 to L-1 Dynamic range of the imaging system is defined as ratio of maximum measurable intensity to the minimum detectable intensity level in the system. Upper limit is determined by the saturation and lower limit is Noise. Contrast is defined as difference in intensity between highest and lowest intensity level in the image. When the dynamic range is very high, then the image is said to have high contrast.
Representing Digital Images The total number of bits required to store a digitized MxN image is b=m x N x k For M=N image b=n 2 k
Spatial resolution Measure of smallest discernible detail in an image. Line pairs per unit distance Dots (pixels) per unit distance (dpi) 1250 dpi 300 dpi 150 dpi 72 dpi
Intensity Resolution 256 128 No. of samples remains same 16 8 64 32 4 2
Intensity Resolution 256 128 In this level=32, you can see imperceptible set of very fine ridge like structures in areas of constant or nearly constant intensity (skull area) 64 32 This is because of the insufficient number of intensity levels in smooth areas of digital image, this is also called as false contouring.
Intensity resolution 16 8 False contouring is visible in the level 16 and below 4 2
Intensity resolution Is there any relation between N and k? Study by Haung [1965], attempted to quantify experimentally the effects on image quality obtained by varying N and k simultaneously. Relatively low detail Intermediate detail Large amount of detail isopreference curve in Nk plane
Image interpolation Used in the tasks such as zooming, shrinking, rotating and geometric corrections. Resampling techniques are used Interpolation is the process of using known data to estimate values of the unknown locations
Image interpolation Resampling Method This will give zooming and shrinking effect Nearest Neighbor interpolation Let us consider 4x4 image shown below 34 30 23 25 20 26 10 28 25 32 30 35 12 34 35 25 Enlarge this image to 8x8 34 34 30 30 23 23 25 25 34 34 30 30 23 23 25 25 20 20 26 26 10 10 28 28 20 20 26 26 10 10 28 28 25 25 32 32 30 30 35 35 25 25 32 32 30 30 35 35 12 12 34 34 35 35 25 25 12 12 34 34 35 35 25 25
Image interpolation Portion of the image Zoomed image
Image interpolation
Image interpolation Bilinear interpolation Makes use of 4 nearest neighbors to estimate the intensity at a given location Let L=8 and l=6 A=23 and B=30 What is the value of Y