1. Document Image Processing
Geometrical Transforms
Linear Filters
Morphological Operations
Connected Component Labeling
Binarization
Contour Tracing
X-Y Cuts
Smearing
Fourier Transform
Hough Transform
Docstrum
Moments and Features

2. Transform Invariants
Geometric Transforms

3. Affine Transforms
Affine transforms cover a linear combination of translations, scale, and rotation
I(x,y) is the original image
I’(x’,y’) is the transformed image
Type
Properties
Meaning
Translation
aij = 0; i,j = 1,2
Scaling
a12=a21=0
Rotation
a11= a12=-
a21= a22=
Slant
a11= a12=
a21= a22= 1
: rotation angle
: slant angle

4. Linear Filters Convolution Equation Smoothing Low pass filter
Vertical Line Sensitive filter
Vertical edge
Sensitive filter
Enhancement filter
Laplacian Edge Operator

5. Morphological Operators

6. Dilation
For each background pixel superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel position.
If at least one pixel in the structuring element coincides with a foreground pixel in the image underneath, then the input pixel is set to the foreground value.
If all the corresponding pixels in the image are background, however, the input pixel is left at the background value.

7. Erosion
For each foreground pixel superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel position.
If every pixel in the structuring element coincides with a foreground pixel in the image underneath, then the input pixel is left as is.
If any pixel coincides with background, however, the input pixel is changed to background.

8. Opening and Closing
Opening: Erosion followed by Dilation using the same kernel
Closing: Dilation followed by Erosion using the same kernel

9. Hit and Miss Kernel has 1s, 0s, and don’t-care
If the 1s and 0s in the kerenel exactly match 1s and 0s in image, then the pixel underneath the origin is set to 1 else 0
Corner finding kernels
Final result is “OR” of the outputs
used to locate isolated points in a binary image.
used to locate the end points on a binary skeleton -four hit-and-miss passes - one for each rotation
used to locate the triple points (junctions) on a skeleton.

10. Thinning
NT(P1) = no. of 0 to 1 transitions in the ordered sequence ,<P2, P3, P9, P2>
NZ(P1) = no. of non-zero neighbors of P1
Set P1 to 0
If 1<NZ(P1)<7 AND
If NT(P1) = 1 AND
P2.P4.P8 = 0 OR NT(P2) .NE. 1 AND
P2.P4.P6 = 0 OR NT(P4) .NE. 1
Use both kernels and their 90o variations
Consider all pixels on the boundaries of foreground regions. Delete pixel that has more than one foreground neighbor, as long as doing so does not locally disconnect
Iterate until convergence.

11. Vornoi Diagrams and Convex Hulls
Thickening can be performed by thinning the background
Convex hull of a binary shape can be visualized by imagining stretching an elastic band around the shape. The elastic band will follow the convex contours of the shape, but will `bridge' the concave contours.
1a and 1b are used for skeletonization of background.
On each thickening iteration till convergence, each element is used in turn, and in each of its 90° rotations.
Structuring elements 2a and 2b are used similarly to prune the skeleton until convergence to get VORNOI diagram.

12. Connected Component Labeling
Scan the image by moving along a row reach a point p to be labeled
Examines neighbors of p which have already been encountered in the scan
(i) to the left of p, (ii) above it, and (iii and iv) the two upper diagonal terms.
If all four neighbors are 0, assign a new label to p
else if only one neighbor is 1 assign its label to p
else if one or more of the neighbors are 1 assign one of the labels to p and note the equivalences.
After completing the scan, the equivalent label pairs are sorted into equivalence classes and a unique label is assigned to each class.

13. Binarization

14. Adaptive Thresholding
Adaptive (T= mean) threshold with 7x7 neighborhood
Original gray scale
Global threshold
Adaptive (T=mean-C) threshold with 7x7 neighborhood; C=7 and C=10
Using T= median instead of the mean

15. Contour Tracing

16. Chain Code Contours

17. Features Geometrical Features Structural Features Moments
Sizes in x and y direction, aspect ratio, perimeter, area
Maximum and minimum distances from boundary to center of mass
Compactness = Perimeter2 / (4 Pi . Area)
Signatures = projection profiles
Structural Features
Number of holes
Euler Number = no. of components – no. of holes
Moments
= area of the object
= center of mass

18. X-Y Cuts
Autocorrelation function of the projection profile, k is the lag parameter
If k=kp is the first peak following the peak at k=0, sharpness of peak is given by

20. Smearing Run Length Smearing (RLS)
Change runs of white pixels of length below a threshold to black
Vertical RLS and AND
Horizontal RLS

21. Fourier Transform

22. Document Images and FT

23. Hough Transform
Parametric Form
Global
Peaks in Accumulator Space

25. Docstrum Slope Histograms Use local information
Connect a mark (component) with K (=4..6) neighbors
Histogram of the slopes
More efficient than projection profiles
Docstrum is the radius and angle plot of the slopes