Spatial Convolution   (Blurring)                                                                                                                                                                                                                                                     

 Example 1                                                                                                                                 

 Create an average filter and move it over an image. Display the new image.

 Solution                                                                                                                                    

im = imread('testpat2.tif');

imshow(im)

avfilter = fspecial('average',[21 21]);

 Result                                                                                                                                       

 Spatial Convolution   (Blurring)                                                                                                                                                                                                                                                     

 Example 2                                                                                                                                 

 Create an average filter and move it over an image. Display the new image.

 Solution                                                                                                                                    

me = imread('zeeya2.bmp');

avfilter = fspecial('average',[3 3]);

 Result                                                                                                                                       

 Gaussian Smoothing                                                                                                                                                                                                                                                                     

 Example  3                                                                                                                                

 Create a Gaussian filter of 25x25 with standard deviation 4 and repeat the above process with this filter.

 Solution                                                                                                                                    

im = imread('testpat2.tif');

imshow(im)

gfilter = fspecial('gaussian',[25 25],4);

 Result                                                                                                                                       

 Gaussian Smoothing                                                                                                                                                                                                                                                                     

 Example  4                                                                                                                                

 Repeat above example on another image.

 Solution                                                                                                                                     

me = imread('zeeya2.bmp');

gfilter = fspecial('gaussian',[3 3],1);

 Result                                                                                                                                        

 Convolution in Frequency Domain                                                                                                                                                                                                                                                 

 Example  5                                                                                                                                

 Make Gaussian filter (256x256) with standard deviation 4. Generate 2D Fourier Transform of the filter. Read any image and take its Fourier Transform and apply the filter to the image by multiplying the FFT of the image and the FFT of the filter together.

 Solution                                                                                                                                     

 Result                                                                                                                                        

 Fourier Transform of an averaging filter                                                                                                                                                                                                                                        

 Example  7                                                                                                                                

 Construct an average filter, but instead of using the 'fspecial' function use the following commands to construct a filter with the same size as the image(256x256 in this case), with a (say) 21x21 square averaging region in the middle.

 Solution                                                                                                                                     

 Result                                                                                                                                        

 Task #1                                                                                                                                    

I would like the following:

a) An image of yourself, your FFT, the FFt of a Gaussian smoothing filter, the product of your FFT and the filter, and the final smoothed image. (Choose a Gaussian filter standard deviation other than 4 pixels)

b) A sequence of images as above but using an averaging filter.

c) A listing of the MATLAB commands you used to do the above tasks (or the function/script you might have written to do this).

 Solution                                                                                                                                     

me = imread('zeeya2.bmp');

gfilter = fspecial('gaussian',[168 120],3);

 Result                                                                                                                                        

Note: The IFFT of  the product of FFTs produced blank image due to only displayed real part of complex data ( warning message displayed is "Displaying real part of complex input")

 HELP                                                                                                                                       

 FSPECIAL                                                                                                                               

  FSPECIAL Create predefined filters.
H = FSPECIAL(TYPE) creates a two-dimensional filter H of the specified type. (FSPECIAL returns H as a computational molecule, which is the appropriate form to use with FILTER2.)

TYPE is a string having one of these values:
'gaussian' for a Gaussian lowpass filter
'sobel' for a Sobel horizontal edge-emphasizing filter
'prewitt' for a Prewitt horizontal edge-emphasizing filter
'laplacian' for a filter approximating thetwo-dimensional Laplacian operator
'log' for a Laplacian of Gaussian filter
'average' for an averaging filter
'unsharp' for an unsharp contrast enhancement filter
Depending on TYPE, FSPECIAL can take additional parameters which you can supply. These parameters all have default values.
H = FSPECIAL('gaussian',N,SIGMA) returns a rotationally symmetric Gaussian lowpass filter with standard deviation SIGMA (in pixels). N is a 1-by-2 vector specifying the number of rows and columns in H. (N can also be a scalar, in which case H is N-by-N.) If you do not specify the parameters, FSPECIAL uses the default values of [3 3] for N and 0.5 for SIGMA.
H = FSPECIAL('sobel') returns this 3-by-3 horizontal edge finding and y-derivative approximation filter:
[1 2 1;0 0 0;-1 -2 -1].
To find vertical edges, or for x-derivates, use -h'.
H = FSPECIAL('prewitt') returns this 3-by-3 horizontal edge finding and y-derivative approximation filter:
[1 1 1;0 0 0;-1 -1 -1].
To find vertical edges, or for x-derivates, use -h'.
H = FSPECIAL('laplacian',ALPHA) returns a 3-by-3 filter approximating the shape of the two-dimensional Laplacian operator. The parameter ALPHA controls the shape of the Laplacian and must be in the range 0.0 to 1.0. FSPECIAL uses the default value of 0.2 if you do not specify ALPHA.
H = FSPECIAL('log',N,SIGMA) returns a rotationally symmetric Laplacian of Gaussian filter with standard deviation SIGMA (in pixels). N is a 1-by-2 vector specifying the number of
rows and columns in H. (N can also be a scalar, in which case H is N-by-N.) If you do not specify the parameters, FSPECIAL uses the default values of [5 5] for N and 0.5 for SIGMA.
H = FSPECIAL('average',N) returns an averaging filter. N is a 1-by-2 vector specifying the number of rows and columns in H. (N can also be a scalar, in which case H is N-by-N.) If you do not specify N, FSPECIAL uses the default value of [3 3].
H = FSPECIAL('unsharp',ALPHA) returns a 3-by-3 unsharp contrast enhancement filter. FSPECIAL creates the unsharp filter from the negative of the Laplacian filter with parameter ALPHA. ALPHA controls the shape of the Laplacian and must be in the range 0.0 to 1.0. FSPECIAL uses the default value of 0.2 if you do not specify ALPHA.

Example
I = imread('saturn.tif');
h = fspecial('unsharp',0.5);
I2 = filter2(h,I)/255;
imshow(I), figure, imshow(I2))

 SURF                                                                                                                                         SURF 3-D colored surface.
SURF(X,Y,Z,C) plots the colored parametric surface defined by four matrix arguments. The view point is specified by VIEW. The axis labels are determined by the range of X, Y and Z, or by the current setting of AXIS. The color scaling is determined by the range of C, or by the current setting of CAXIS. The scaled color values are used as indices into the current COLORMAP. The shading model is set by SHADING.
SURF(X,Y,Z) uses C = Z, so color is proportional to surface height.
SURF(x,y,Z) and SURF(x,y,Z,C), with two vector arguments replacing the first two matrix arguments, must have length(x) = n and length(y) = m where [m,n] = size(Z). In this case, the vertices of the surface patches are the triples (x(j), y(i), Z(i,j)). Note that x corresponds to the columns of Z and y corresponds to the rows.
SURF(Z) and SURF(Z,C) use x = 1:n and y = 1:m. In this case, the height, Z, is a single-valued function, defined over a geometrically rectangular grid.
SURF(...,'PropertyName',PropertyValue,...) sets the value of the  specified surface property. Multiple property values can be set with a single statement.
SURF returns a handle to a SURFACE object.
AXIS, CAXIS, COLORMAP, HOLD, SHADING and VIEW set figure, axes, and  surface properties which affect the display of the surface.

 FFT2                                                                                                                                        

FFT2 Two-dimensional discrete Fourier Transform.
FFT2(X) returns the two-dimensional Fourier transform of matrix X. If X is a vector, the result will have the same orientation.
FFT2(X,MROWS,NCOLS) pads matrix X with zeros to size MROWS-by-NCOLS before transforming.          

 IFFT2                                                                                                                                       

 IFFT2 Two-dimensional inverse discrete Fourier transform.
IFFT2(F) returns the two-dimensional inverse Fourier transform of matrix F. If F is a vector, the result will have the same orientation.
IFFT2(F,MROWS,NCOLS) pads matrix F with zeros to size MROWS-by-NCOLS before transforming.

 IMPROFILE                                                                                                                            

IMPROFILE Compute pixel-value cross-sections along line segments.
IMPROFILE computes the intensity values along a line or a multiline path in an image. IMPROFILE selects equally spaced points along the path you specify, and then uses interpolation to find the intensity value for each point. IMPROFILE works with grayscale intensity images and RGB images.
If you call IMPROFILE with one of these syntaxes, it operates interactively on the image in the current axes:
C = IMPROFILE
C = IMPROFILE(N)
N specifies the number of points to compute intensity values for. If you do not provide this argument, IMPROFILE chooses a value for N, roughly equal to the number of pixels the path traverses.
You specify the line or path using the mouse, by clicking on points in the image. Press <BACKSPACE> or <DELETE> to remove the previously selected point. A shift-click, right-click, or double-click adds a final point and ends the selection; pressing <RETURN> finishes the selection without adding a point. When you finish selecting points, IMPROFILE returns the interpolated data values in C. C is an N-by-1 vector if the input is a grayscale intensity image, or an N-by-1-by-3 array if the input image is an RGB image.
If you omit the output argument, IMPROFILE displays a plot of the computed intensity values. If the specified path consists of a single line segment, IMPROFILE creates a two-dimensional plot of intensity values versus the distance along the line segment; if the path consists of two or more line segments, IMPROFILE creates a three-dimensional plot of the intensity values versus their x- and y-coordinates.
You can also specify the path noninteractively, using these syntaxes:
C = IMPROFILE(I,xi,yi)
C = IMPROFILE(I,xi,yi,N)
xi and yi are equal-length vectors specifying the spatial coordinates of the endpoints of the line segments.
You can use these syntaxes to return additional information:
[CX,CY,C] = IMPROFILE(...)
[CX,CY,C,xi,yi] = IMPROFILE(...)
CX and CY are vectors of length N, containing the spatial coordinates of the points at which the intensity values are computed.
To specify a nondefault spatial coordinate system for the input image, use these syntaxes:
[...] = IMPROFILE(x,y,I,xi,yi)
[...] = IMPROFILE(x,y,I,xi,yi,N)
x and y are 2-element vectors specifying the image XData and YData.
[...] = IMPROFILE(...,METHOD) uses the specified interpolation method. METHOD is a string that can have one of these values:
'nearest' (default) uses nearest neighbor interpolation
'bilinear' uses bilinear interpolation
'bicubic' uses bicubic interpolation
If you omit the METHOD argument, IMPROFILE uses the default method of 'nearest'.
 

Class Support
The input image can be of class uint8, uint16, or double. All other inputs and outputs are of class double.

Example
I = imread('alumgrns.tif');
x = [35 338 346 103];
y = [253 250 17 148];
improfile(I,x,y), grid on

 FILTER2                                                                                                                                  

FILTER2 Two-dimensional digital filter.
Y = FILTER2(B,X) filters the data in X with the 2-D FIR filter in the matrix B. The result, Y, is computed
using 2-D correlation and is the same size as X.
Y = FILTER2(B,X,'shape') returns Y computed via 2-D correlation with size specified by 'shape':
'same' - (default) returns the central part of the correlation that is the same size as X.
'valid' - returns only those parts of the correlation that are computed without the zero-padded edges, size(Y) < size(X).
'full' - returns the full 2-D correlation, size(Y) > size(X).
FILTER2 uses CONV2 to do most of the work. 2-D correlation is related to 2-D convolution by a 180 degree rotation of the filter matrix.

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