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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.

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.

The median filter REPLACES the value of a PIXEL by the median of the GRAY LEVELS in the NEIGHBORHOOD of that pixel.

The median filter replaces the value of a pixel by the median of the gray levels in the neighborhood of that pixel.

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 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.

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.

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.

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

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 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.

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.

The negative of an IMAGE with gray levels in the range [0, L-1] is OBTAINED by using the negative TRANSFORMATION, which is given by the expression.

s = L-1-r

Where s is OUTPUT pixel.

r is INPUT pixel.

The negative of an image with gray levels in the range [0, L-1] is obtained by using the negative transformation, which is given by the expression.

s = L-1-r

Where s is output pixel.

r is input pixel.

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.

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.

Image ENHANCEMENT at any Point in an image DEPENDS only on the GRAY level at that point is often referred to as Point PROCESSING.

Image enhancement at any Point in an image depends only on the gray level at that point is often referred to as Point processing.

The categories of Image ENHANCEMENT are

1. Spatial DOMAIN
2. Frequency domain Spatial domain: It refers to the image plane, itself and it is based on DIRECT manipulation of pixels of an image.

Frequency domain techniques are based on modifying the Fourier transform of an image.

The categories of Image Enhancement are

Frequency domain techniques are based on modifying the Fourier transform of an image.

Image ENHANCEMENT is to PROCESS an image so that the output is more SUITABLE for specific application.

Image enhancement is to process an image so that the output is more suitable for specific application.

• Real and orthogonal
• Very fast transform
• Basis vectors are SEQUENTIALLY ORDERED
• Has FAIR energy COMPACTION for IMAGE
• Useful in feature extraction,image coding and image analysis problem

N = 4 = 2N

=> n = 2

N = 4 = 2n

=> n = 2

• Separability
• Translation
• PERIODICITY and Conjugate PROPERTY
• ROTATION
• DISTRIBUTIVITY and scaling
• Average value
• CONVOLUTION and Correlation
• Laplacian

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.

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.

1. REMOTE SENSING
2. Image transmission and storage for business APPLICATION
3. Medical IMAGING
4. Astronomy

The digital IMAGE is an array of REAL or complex NUMBERS that is represented by a FINITE no of bits.

The digital image is an array of real or complex numbers that is represented by a finite no of bits.

Since MEAN square ERROR of reconstructed image and ORIGINAL image is minimum and the mean value of TRANSFORMED image is zero so that uncorrelated.

Since mean square error of reconstructed image and original image is minimum and the mean value of transformed image is zero so that uncorrelated.

KL Transform 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 transform.

KL Transform 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 transform.

1. Slant TRANSFORM is real and ORTHOGONAL.
2. Slant transform is a fast transform
3. Slant transform has very good energy compaction for IMAGES
4. The basic vectors of Slant matrix are not sequency ordered.

1. Haar transform is REAL and orthogonal.
2. Haar transform is a very fast transform
3. Haar transform has very POOR energy COMPACTION for images
4. The basic VECTORS of Haar MATRIX sequency ordered.

Hadamard transform 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

Hadamard transform 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

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.

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.

1. Hadamard TRANSFORM contains any one VALUE.
2. No MULTIPLICATIONS are REQUIRED in the transform calculations.
3. The no: of additions or subtractions required can be reduced from N^2 to Nlog2N
4. Very good energy compaction for highly correlated images.

1. REAL, symmetric and orthogonal.
2. Not the IMAGINARY PART of the unitary DFT.
3. FAST TRANSFORM.

1. Real & orthogonal.
2. FAST TRANSFORM.
3. Has EXCELLENT energy compaction for highly CORRELATED data

The NXN cosine transform c(k) is CALLED the discrete cosine transform 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 NXN cosine transform c(k) is called the discrete cosine transform 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

1. Symmetric
2. Periodic extensions
3. SAMPLED FOURIER TRANSFORM
4. Conjugate SYMMETRY.

1. The DFT and unitary DFT matrices are symmetric.
2. The EXTENSIONS of the DFT and unitary DFT of a SEQUENCE and their inverse TRANSFORMS are periodic with period N.
3. The DFT or unitary DFT of a real sequence is conjugate symmetric about N/2.

1. PERIODICITY

WN^(K+N)= WN^K

2. SYMMETRY

WN^(K+N/2)= -WN^K

1. Periodicity

WN^(K+N)= WN^K

2. Symmetry

WN^(K+N/2)= -WN^K

FORWARD TRANSFORM

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 TRANSFORMS

X(n) = (1/N) (k=0 to N-1) _ x(k) exp(-j 2* pi* nk/N) ; n= 0,1,2,…N-1

Forward transform

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 transforms

X(n) = (1/N) (k=0 to N-1) _ x(k) exp(-j 2* pi* nk/N) ; n= 0,1,2,…N-1

1. Determinant and the Eigen VALUES of a unitary matrix have unity magnitude
2. The ENTROPY of a random VECTOR is preserved under a unitary Transformation
3. Since the entropy is a MEASURE of average information, this means information is preserved under a unitary transformation.

TRANSPOSE of MATRIX = INVERSE of a matrix. Orthoganality.

Transpose of matrix = Inverse of a matrix. Orthoganality.

1. To REDUCE BAND WIDTH
2. To reduce redundancy
3. To EXTRACT feature.

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 transform provides a set of coordinates or basis vectors for vector space.

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 transform provides a set of coordinates or basis vectors for vector space.

LUMINANCE measured in lumens (lm), gives a measure of the amount of ENERGY an observer perceiver from a LIGHT SOURCE.

Luminance measured in lumens (lm), gives a measure of the amount of energy an observer perceiver from a light source.

RADIANCE is the total amount of ENERGY that FLOWS from the light source, and it is usually MEASURED in watts (w).

Radiance is the total amount of energy that flows from the light source, and it is usually measured in watts (w).

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.

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.

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.

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.

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

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

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)

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)

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.

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.

Gray LEVEL refers to a SCALAR measure of intensity that RANGES from black to grays and finally to white.

Gray level refers to a scalar measure of intensity that ranges from black to grays and finally to white.

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.

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.

Brightness of an object is the PERCEIVED luminance of the SURROUND. TWO objects with different SURROUNDINGS would have IDENTICAL luminance but different brightness.

Brightness of an object is the perceived luminance of the surround. Two objects with different surroundings would have identical luminance but different brightness.

The SPATIAL interaction of Luminance from an object and its SURROUND CREATES a Phenomenon CALLED the mach band effect.

The spatial interaction of Luminance from an object and its surround creates a Phenomenon called the mach band effect.

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.

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.

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.

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.

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.

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.