Image Processing (EA C443)

Transcription

1 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

2 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

3 Image Formation Model Image data in the form of matrix, which is a 2D function f(x,y)

4 Simple Image acquisition model Light Source Photo detector DIGITIZATION DIGITAL IMAGE

5 Image Model Image Model Spatial coordinates 0 to f ( x, y) i( x, y) r( x, y) 0 to 1 Incident component Reflected component

6 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

7 DIGITIZATION (SAMPLING) Digitizing the coordinates values is called as sampling Pixel at coordinate (x,y) or at m th row and n th column

8 Image Sampling and Quantization Digitizing the amplitude values is called as quantization

9 Image Sampling and Quantization Image before sampling and quantization Image after sampling and quantization

10 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.

11 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.

12 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.

13 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

14 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

15 Intensity Resolution No. of samples remains same

16 Intensity Resolution 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) This is because of the insufficient number of intensity levels in smooth areas of digital image, this is also called as false contouring.

17 Intensity resolution 16 8 False contouring is visible in the level 16 and below 4 2

18 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

19 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

20 Image interpolation Resampling Method This will give zooming and shrinking effect Nearest Neighbor interpolation Let us consider 4x4 image shown below Enlarge this image to 8x

21 Image interpolation Portion of the image Zoomed image

22 Image interpolation

23 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