103 With 

   103 Lets us try to use these concepts of slicing and striding for doing some basic image manipulation

   104 

   105 pylab has a function imread to read images. We will use '(in)famous' lena image for our experimentation. Its there on desktop. 

   106 

   107 a = imread('lena.png')

   108 a is a numpy array with the 'RGB' values of each pixel

   109 a.shape

   110 

   111 its a 512x512x3 array.

   112 

   113 to view the image write

   114 imshow(a)

   115 

   116 lets try to crop the image to top left quarter. Since a is a normal array we can use slicing to get top left quarter by

   117 imshow(a[:255,:255]) (half of 512 is 256)

   118 

   119 But hat is not 'interesting' part of lena. Lets crop the image so that only her face is visible. for that we will need some rough estimates of pixels. 

   120 imshow(a)

   121 now move your mouse cursor over the image, it will give us x, y coordinates where ever we take our cursor. We can get rough estimate of lena's face now cropping to those boundaries is simple

   122 imshow(a[200:400, 200:400])

   123 

   124 Next we will try striding on this image. We will resize the image by skipping each alternate pixel. We have already seen how to skip alternate elements so,

   125 imshow(a[::2, ::2])

   126 note now the size of image is just 256x256 and still quality of image is not much compromised.

   127 -------------------------

   128 

   129 Till now we have covered initializing and accessing elements of arrays. Now we shall concentrate on functions available for arrays. We start this by creating 4x4 array by

   130 

   131 a = array([[ 1, 1, 2, -1],[ 2, 5, -1, -9], [ 2, 1, -1, 3], [ 1, -3, 2, 7]])

   132 a

   133 

   134 To get transpose of this matrix write

   135 a.T

   136 sum() function returns sum of all the elements of a matrix.

   137 sum(a)

   138 

   139 lets create one more array for checking more operations

   140 b = array([[3,2,-1,5], [2,-2,4,9], [-1,0.5,-1,-7], [9,-5,7,3]])

   141 

   142 + will take care of matrix additions

   143 a + b

   144 

   145 lets try multiplication now, 

   146 a * b will return element wise product of two matrices.

   147 

   148 To get matrix product of a and b we use

   149 dot(a, b)

   150 

   151 and to get inverse of matrix 

   152 

   153 inv(a)

   154 

   155 det(a) returns determinant of matrix a

   156 

   157 we shall create one array e

   158 e = array([[3,2,4],[2,0,2],[4,2,3]])

   159 and then to evaluate eigenvalues of array

   160 eig(a)

   161 it returns both eigen values and eigen vector of given matrix

   162 to get only eigen values use

   163 eigvals(a)

   164 

   165 This brings us to end of this session. We have covered Matrices

   166 Initialization

   167 Slicing

   168 Striding

   169 A bit of image processing

   170 Functions available for arrays

   171 Thank you