计算机视觉课(5)

i j
for all B[.,.] = 1 pixels.
(2) position: the position of a bina by its mass center.
jB[i, j ] x B[i, j ]
i j i j
iB[i, j] y B[i, j ]
i j
Set
,0 and
2
2 0
We get: where
x, y is the center of the component,
1 1 b tan ( ) 2 ac
2 i j
x cos y sin
and
where
a ( xij x) B[i, j ];
i j i j
(3)Orientation:
The orientation of binary image component is defined by a straight line that the distance sum from all the pixels to the line is minimized,i.e.,
1. Neighbors/path/connectivity (1) Neighbors of a pixel
a. 4-neighbors: the upper, lower, left and right neighbor pixels of a pixel.
b. 8-neighbors: the 4-neighbors pixels plus the diagonal neighbors.
r B[i, j ] min
2 2 ij i j
where
ri , j
is the distance from pixel [ i, j ]to the line.
Let the line in polar coordinates be:
Then: So:
x cos y sin r x cos y sin 2 2 ( xij cos yij sin ) B[i, j ]
jk ]
(3) Connectivity: A pixel p is said to be connected to q if there is a path from p to q consisting of pixels of S Connected component: A set of pixels in which each pixel is connected to all other pixels of the set.
b 2 ( xij x)( yij y ) B[i, j ];
c ( yij y )2 B[i , j ];
i j
i
j
Note:
The
has two values; the corresponding lines are
x 2 may minimize or maximize
Course 3
Binary Image
Course 3
Binary Image
Binary Images have only two gray levels:
“1” and “0”, i.e., black / white.
—— save memory
—— fast processing
—— many features of an intensity image appear in binary form, e.g. edge, contour, … —— human can understand binary line drawings.

.
4-connected
8-connected
2. Geometric attributes of a binary image/component: (1) size (area):
A B[i, j ]
j0 ]
to the pixel [in , jn ] is a
[i0 , j0 ],[i1 , j1 ],,[in , jn ]
where the pixel [ik 1 , jk 1 ] is a neighbor of pixel [ik , for all 0 k n 1 . ——4 path if 4-neighbor is used ——8 path if 8-neighbor is used
2.
called maximum axis and minimum axis of the image
component.
Maximum axis
Minimum axis
(4) Foreground / Background : Foreground: the set f all “1” pixels in an image. Background: the set of all connected components of S that have points on the border of the image. Hole: the connected component in S not have border points. but it does 0 Note: foreground and background 1 must use different connectivities. 0 Hole or not? 1 0 1 0 1 0
[i-1,j] [i,j-1] [i,j] [i,j+1] [i-1,j-1] [i,j-1] [i-1,j] [i,j] [i-1,j+1] [i,j+1]
[i+1,j]
4-neighbor
[i+1,j-1]
[i-1,j]
8-neighbor
[i+1,j+1]
(2) Path A path form pixel [i0 , sequence of pixel indices: