Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Hold-And-Modify wikipedia , lookup
Indexed color wikipedia , lookup
Convolution wikipedia , lookup
Scale space wikipedia , lookup
Stereoscopy wikipedia , lookup
Edge detection wikipedia , lookup
Anaglyph 3D wikipedia , lookup
Image editing wikipedia , lookup
Ringing artifacts wikipedia , lookup
Histogram statistics for image enhancement Let r denote a discrete random variable representing intensity representing intensity values in [0, L-1] and let p(ri)denote the normalised histogram component corresponding to value r .We may view p(ri ) as an estimate of the probability that infinity ri occurs in the image µn= ( − ) p( ) nth moment about its mean m is the mean(average intensity) m =∑ r p( ) µl = ( − ) p( ) = Global mean and variance a computed on an entire image and a useful for gross adjustment in overall intensity and contrast. A more powerful use of these parameters is in local enhancement, where local mean and variance are used as the basis for making changes. S xy denote a neighbourhood of a specified useful(x, y). The mean value of the pixel is given by =∑ ( ) = (r − m ) ( ) Enhance the dark area while leaving the light area unchanged as possible. Fundamentals of spatial filtering:Filtering is useful for amplifying (passing) or rejecting certain frequency components. w(-1, 1) w(0, -1) w(1,- 1) w(-1, 0) w(0,0) w(1, 0) w(-1, 1) w(0,1) w(1,1) Filter that passes low frequency is called low pass. The net effect produced by a low pass filter is to blur (smooth) the image. we can accomplish a similar smoothing directly on the image itself by using spatial filter .There is a linear one –to-one correspondence between linear spatial filters and filters in the frequency domain. spatial filtering is more versatile than the filtering in the frequency domain as spatial filtering can be used for non-linear filtering. The mechanics of spatial filtering:Spatial filter consists of (1) a neighbourhood, (2) a predefined operation that is performed on the image pixels encompassed by the neighbourhood. Linear and non-linear filtersAt any point (x, y) is the image, the response g(x, y) of the filter is the sum of products of the filter coefficient and the pixels encompassed by filters. For a mask of m x n, we assume that m= 2n+1 and n=2b+1 where a, b a position integers. In general, linear spatial filtering of an image of size M x N with filter size m x n is given by g (x, y)=∑ ∑ ( , ). ( + , + ). Spatial correlation and convolution:There are two clearly related concepts in linear filtering. One is correlation and other is convolution. Correlation is the process of moving the filter mask on the image and computing the sum of products of at each location. The mechanism of convolution is the sum, except that the filter is first related by 180 (a) (b) 0 0 0 1 0 0 0 0 w= 1 2 3 2 8 0000000100000000 12328 →00082321000 Full correlation Correlation is a function of displacement of the filter Correlating a filter w with a function that contains a single 1with the rest being 0’s result that is a copy of w rotated by 180ᵒ If the filter mask is symmetric correlation and convolution yield the same result Correlation can be used to find matches between images W(x,y).f(x,y)=∑ ∑ ( , ). ( + , + ) a= (m-1)/2, n= (n-1)/2 are odd integers, W(x, y)* f(x, y) → convolution ( , ) ( − , − ) Exercise (1) In some applications it is useful to model the histogram of input images as Gaussian probability density function as – pr (r) = √ . ( ) Ϭ What is the transformation function you would use for histogram normalization? Hint: S=T (Ϭ) = (L-1)∫ = (L-1)∫ (w)dw ( √ Ϭ ) Ϭ dw Exercise (2) Suppose that a digital image is subjected to histogram equalization. Show that a second pass of histogram equalization (on the histogram equalized image) will produce exactly the same result as the first pass.