 Hello friends, myself, Darshan Pandit, Assistant Professor, Department of Computer Science and Engineering from Walchand Institute of Technology, Solapur. So, today we are going to discuss about half-toning techniques in computer graphics. So, the learning outcome is like at the end of this session student will be able to differentiate various half-toning techniques. So in this we are going to see what is image representation after that quantization, after that different techniques that is classical half-toning and digital half-toning. So image representation is nothing like a image is a 2D rack linear array of pixels. So this is how image is represented. So modification in digital image 1, so we will get digital image 2 and improvement in some digital image 2 we will get digital image 3. So here you can see the difference between continuous image and digital image. So here a pixel is a sample not just a square. So in image resolution we are having intensity, spatial and temporal resolution. So intensity resolution where each pixel has only depth bits for color or intensity. So spatial resolution images has only width into height pixels and temporal resolution monitors refresh image at only hertz that is rate that is refresh rate is counted here in temporal resolution. So there are errors, the intensity quantization error occurs when not enough intensity resolution is there and spatial aliasing error occurs when not enough spatial resolution is provided and temporal aliasing error occurs when not enough temporal resolution is provided. So here quantization is nothing but the artifact due to limited intensity resolution where frame buffers have limited number of bits per pixel and physical device have limited dynamic range. So here uniform quantization you can see in the figure that is uniform quantization where images with decreasing bits per pixels are given. So you can see the difference between 8-bit, 4-bit, 2-bit and 1-bit. So here many displays and hard copy devices are by level. They can only produce two intensity levels. So in such display or hard copy devices we can create an apparent increase in number of available intensities. So this is achieved by incorporating multiple pixel position into display of each intensity value. So when we view a small area from a sufficient large viewing distance our eyes average fine details with a small area and record only the overall intensity of the area. So the phenomenon of apparent increase in number of available intensity by considering combined intensity of multiple pixel is known as halftoning. So the halftoning is commonly used in printing black and white photographs in newspaper, magazines and books. So the pictures produced by halftoning process are called as halftones. In computer graphics halftone reproduction are approximated using rectangular pixels, regions say you can 2 by 2 pixels or 3 by 3 pixels. So these regions are called as halftone patterns or pixel patterns. So the figure shown the halftone pattern to create number of intensity levels. So here you can see dots of varying size to represent intensity. So the area of dots proportional to the intensity in the image. So here figure B shows halftone with respect to figure A. So figure A shows how the human eye would see the sort of arrangement of pixels from a sufficient distance. So these are the examples of halftone patterns. So newspaper image, so when you zoom the newspaper image. So you can see the halftone patterns which is used in a printing process. So typically halftone resolutions are used for printing. So for screen printing it uses 45 to 65 lpi that is line per inch. In laser print it uses 65 lpi and in laser print 600 dpi, dpi is nothing but dot per inch. Uses 85 lpi and offset newspaper print uses 85 lpi and offset coated paper print uses 85 to 185 lpi that is lines per inch. So here digital halftoning is again classified in three types, patterning, dithering and thresholding. Thresholding and error distribution. So here when in patterning when the image is to be displayed or printed on a device with much larger resolution than the original image. So the resolution may be trade off for dynamic range. In printing where dot density is very high this is usually possible. So the idea behind patterning is like device pixels are grouped together in small blocks and various patterns of binary pixels are used as one gray pixel. So in this example you can see patterning of 2 by 2 ditha pattern which use cluster of pixel to represent the intensity. So directly the patterns are given. So here 2 by 2 pixel cell pattern else 5 intensity levels that is 0 to 4. And with multiple dot size 2 by 2 pattern else 9 intensity level. So in this figure you can see 2 by 2 pattern with multiple dot size. So if you are having different dot size that is if you are having varying pixel smaller and larger then it tells 9 intensity levels. So it can also be represented in a matrix form. So p denotes bi-level pattern that is 2 by 2 pattern. So 1, 2, 3 and 4. So this can be represented in this way. So first you are having 1 after that in pattern you can see. So next pixel is at the diagonal 2 after that 3 is the below pixel after that in the diagonal of 3 you are having 4. So in this way there is a matrix representation of 2 by 2 pattern. So in this example you can see 3 by 3 pattern. So 3 by 3 pattern produces 10 possible intensity levels that is 0 to 9. And with multiple dot size 3 by 3 pattern produces 27 intensity levels. So you can see 0 with the 0 intensity and with the 1 intensity. So this 1 intensity is written in the matrix form that is in the second row, second column. So again after that you are having 2, the next pixel is written 2 after that 3. So above the 1 you are having third pixel. So it has been denoted here. So in this way we can generate a matrix representation for 3 by 3 pattern. P3 is nothing but 3 by 3 pattern. So from 0 to 9 intensity levels they are given. And for n by n group of bi-level pattern it requires n square plus n 1 intensity levels. So the previous arrangement uses cells of 4 pixel sheets and else 5 possible grey levels. So here the disadvantage of patterning is that loss of spatial resolution, making it acceptable only if resolution of the image is lower than the resolution of the display. The use of patterning with the previous cells results new image with double dimension to obtain 256 by 256 new image. So we have to use 128 by 128 original image. So here you can pause the video and just write the answer. So question is like what is the intensity level produced by 8 by 8 pixel pattern? So the answer is like 65 intensity levels will be produced by 8 by 8 pixel pattern. As we know n by n group of pixel pattern generates n square plus 1 intensity levels. So after that you are having dithering. So here it distributes errors among the pixels which exploit spatial integration in our eyes. So displays greater range of perceptible intensities. So this error is represented by dither matrix which is compared with the image repeating check board patterns. So the smallest order dither pattern is d2 that is 0, 2, 3, 1. So the 0 is the error added in this pattern. So these are the images which have been showed with the order dithering pattern. So the larger is the dither pattern that is 4 by 4, 8 by 8 and so on. So this can be obtained by the recurrent relationship. So this is the recurrent relationship given. So where n is the matrix size and un is the unity matrix. So the simplest technique for improving visual resolution is to use threshold pattern. So we create the pattern and compare with the original image. So if pixel in the original image exceeds the corresponding pixel then the threshold pattern is replaced by 1 else it is replaced by 0. That is if x, y greater than t then white else black where x, y is the intensity of the image at the pixel x, y and t is the threshold value. So last is you are having error distribution. So in error distribution, quantization error is spread over the neighbor pixel. The error is dispersed to pixels right hand below. So this is how error is dispersed in alpha, beta and gamma terms. So all should be equal to 1. So these are the examples given with the error distribution, how the image is represented with error diffusion and dithering result. So these are the half tone examples. So continuous half tone, dithering and error distribution. So these are the references which are used to create this video. Thank you.