Zooming may be viewed as over sampling. It involves the creation of new pixel locations and the assignment of gray levels to those new locations.
Shrinking may be viewed as under sampling. To shrink an image by one half, we delete every row and column. To reduce possible aliasing effect, it is a good idea to blue an image slightly before shrinking it.
A Mask is a small two-dimensional array, in which the value of the mask coefficient determines the nature of the process, such as image sharpening.
Forward trform
The sequence of x(n) is given by x(n) = { x0,x1,x2,… xN-1}.
X(k) = (n=0 to N-1) _ x(n) exp(-j 2* pi* nk/N) ; k= 0,1,2,…N-1
Reverse trforms
X(n) = (1/N) (k=0 to N-1) _ x(k) exp(-j 2* pi* nk/N) ; n= 0,1,2,…N-1
Gray level refers to a scalar measure of intensity that ranges from black to grays and finally to white.
The output of a smoothing, linear spatial filter is the average of the pixels contain in the neighborhood of the filter mask. These filters are called averaging filters.
The negative of an image with gray levels in the range [0, L-1] is obtained by using the negative trformation, which is given by the expression.
s = L-1-r
Where s is output pixel.
r is input pixel.
Image enhancement at any Point in an image depends only on the gray level at that point is often referred to as Point processing.
Radiance is the total amount of energy that flows from the light source, and it is usually measured in watts (w).
Hadamard trform matrices Hn are NXN matrices where N=2^n , n= 1,2,3,… is defined as Hn= Hn-1 * H1 = H1* Hn-1
= 1/ _ 2 Hn-1 Hn-1
H2 = 1 1
1 –1
If gray levels in a certain range occur frequently while others occurs rarely, the quantization levels are finely spaced in this range and coarsely spaced outside of it.This method is sometimes called Tapered Quantization.
The spatial interaction of Luminance from an object and its surround creates a Phenomenon called the mach band effect.
The intensity or the brightness pattern perceive a darker stribe in region D and brighter stribe in region B.This effect is called Mach band pattern or effect.
An Image may be defined as a two dimensional function f (x,y) where x & y are spatial (plane) coordinates, and the amplitude of f at any pair of coordinates (x,y) is called intensity or gray level of the image at that point. When x,y and the amplitude values of f are all finite, discrete quantities we call the image as Digital Image.
The number of bits required to store a digital image is
b=M X N X k
When M=N, this equation becomes
b=N^2k
Brightness of an object is the perceived luminance of the surround. Two objects with different surroundings would have identical luminance but different brightness.
Trpose of matrix = Inverse of a matrix. Orthoganality.
Image enhancement is to process an image so that the output is more suitable for specific application.
Spatial filtering is the process of moving the filter mask from point to point in an image. For linear spatial filter, the response is given by a sum of products of the filter coefficients, and the corresponding image pixels in the area spanned by the filter mask.
Luminance measured in lumens (lm), gives a measure of the amount of energy an observer perceiver from a light source.
Since mean square error of reconstructed image and original image is minimum and the mean value of trformed image is zero so that uncorrelated.
@Periodicity
WN^(K+N)= WN^K
@Symmetry
WN^(K+N/2)= -WN^K
The range of values spanned by the gray scale is called dynamic range of an image. Image will have high contrast, if the dynamic range is high and image will have dull washed out gray look if the dynamic range is low.
The Haar functions are defined on a continuous interval Xe [0,1] and for K=0,1,……. N-1.Where N=2^n. The integer k can be uniquely decomposed as K=2^P+Q-1.
KL Trform is an optimal in the sense that it minimizes the mean square error between the vectors X and their approximations X^. Due to this idea of using the Eigenvectors corresponding to largest Eigen values. It is also known as principal component trform.
Digitization of spatial coordinates (x,y) is called Image Sampling. To be suitable for computer processing, an image function f(x,y) must be digitized both spatially and in magnitude.
The 100th percentile is maximum filter is used in finding brightest points in an image. The 0th percentile filter is minimum filter used for finding darkest points in an image.
f(x,y )= f(0,0) f(0,1)………………f(0,N-1)
f(1,0) f(1,1)………………f(1,N-1)
.
.
.
f(M-1) f(M-1,1)…………f(M-1,N-1)
Digitizing the amplitude values is called Quantization. Quality of digital image is determined to a large degree by the number of samples and discrete gray levels used in sampling and quantization.
The median filter replaces the value of a pixel by the median of the gray levels in the neighborhood of that pixel.
The digital image is an array of real or complex numbers that is represented by a finite no of bits.
For a function f (x, y), the gradient f at co-ordinate (x, y) is defined as the
vector_f = _f/_x
_f/_y
_f = mag (_f) = {[(_f/_x) 2 +(_f/_y) 2 ]} ½
The NXN cosine trform c(k) is called the discrete cosine trform and is defined as
C(k) = 1/_N , k=0, 0 _ n _ N-1 = _ (2/N) cos (pi (2n+1)/2N 1_ k _ N-1, 0_ n _ N-1
The categories of Image Enhancement are
Frequency domain techniques are based on modifying the Fourier trform of an image.
Resolution is defined as the smallest number of discernible detail in an image. Spatial resolution is the smallest discernible detail in an image and gray level resolution refers to the smallest discernible change is gray level.
The histogram of a digital image with gray levels in the range [0, L-1] is a discrete function h (rk) = nk, where rk is the kth gray level and nk is the number of pixels in the image having gray level rk.
An image can be expanded in terms of a discrete set of basis arrays called basis images. Unitary matrices can generate these basis images. Alternatively, a given NXN image can be viewed as an N^2X1 vectors. An image trform provides a set of coordinates or basis vectors for vector space.
N = 4 = 2n
=> n = 2