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HARRY POTTER MAGIC AND MATRIX


       A table of numbers is a matrix
example:    1 2 3
                   4 5 6
                   7 8 9
A image is made up of number of dots or points or pixels (picture elements).  The rows of dots can be represented as matrix.
example 111 112 114 ...
               200 210 215 ....
               98 97 96 ...
               -- --     --  ...
               --  --    -- ...
    It is a representation of grey scale image. Here, each dot is given some value from 0 to 256.  0 means dark, or black, 256 is bright or white.  Hence, we have converted an image into set of numbers in matrix I.
     If we multiply each number in the matrix by a factor like 1.5, (called scalar multiplication), the values will increase and the image will brighten up.  If you multiply by 0.6, the image would be dimmed.  Now, we are able to control the image with mathematical operations.  The scalar multiplication is written as 1.5 I or 0.6 I.

COLOUR IMAGE
     Using three primary colours namely Red, blue, and green (RBG) we can produce any colour.  So a colour image of 400*600 pixels will have three matrices of size 400*600.  One for each colour.

MAGIC WITH MATRIX
    Harry disappears in a hall.  He slowly fads and dissolves in the hall.  How to enact it using simple math operations.
     Take a photo of a hall and a photo of Harry potter.  Combine them and make it a single photo and call it "B".  Name the empty hall photo as 'F'.  The image that is going to appear on the screen is 'C'.
    Now
  C= x.B +y.F
    x and y can take values from 0 to 1. This formula going to help us to do the magic.
CASE I
    If x=1, and y=0,
we get C=1*B +0*F =B
we will see Harry potter in the hall.
CASE II
  If x=0 and y=1
  we get C=0*B +1*F = F
  We will see only empty hall.
Case III
  If C= 0.75*B +0.25*F
  the image dims-up.
If C=0.5*B+0.5*F
both the images are dimmed.  Harry potter dissolves into the hall.
If c= 0.25*B +0.75*F
Harry almost gone(0.25).  Hall brightens up(0.75).
If C=0*B+1*F= F
Harry completely fads out and only the hall appears
    The same technique can be used to place the harry in another location.  Again same process could be used to suck out the colours from an image.

FLIPPING
    By interchanging rows in an image matrix, an image can be flipped.  Exchange row number 1 and row number n,(n being last row).  row number 2 and row number n-1; 3 and n-2 and on.  The image will be flipped -upside down.
    Now, you can understand how the 'layers' in photo-shop works.  Simple matrix, mathematical operations can manipulate an image in many ways. 
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Comments

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