Binary Image Compression Binary Image Compression Using Efficient Partitioning Using Efficient Partitioning into Rectangular Regionsinto Rectangular Regions

IEEE Transactions on CommunicationsIEEE Transactions on Communications

Sherif A.Mohamed and Moustafa M. Fahmy (IEEE Fellow)Sherif A.Mohamed and Moustafa M. Fahmy (IEEE Fellow)

A New Compression Technique A New Compression Technique for Binary Text Imagesfor Binary Text Images

IEEE Symposium on Computers and Communications (ISCC)IEEE Symposium on Computers and Communications (ISCC)

Azhar Quddus and Moustafa M. Fahmy (IEEE Fellow)Azhar Quddus and Moustafa M. Fahmy (IEEE Fellow)

Binary Image Compression Binary Image Compression Using Efficient Partitioning Using Efficient Partitioning into Rectangular Regionsinto Rectangular Regions

IEEE Transactions on CommunicationsIEEE Transactions on Communications

Sherif A.Mohamed and Moustafa M. Fahmy (IEEE Fellow)Sherif A.Mohamed and Moustafa M. Fahmy (IEEE Fellow)

OutlineOutline• Introduction• Image Partition into Rectangles• Algorithm for Partitioning• Coordinate Data Compression• Test Images of different types and sizes• Experimental Results• Conclusion

IntroductionIntroduction• This paper propose a new binary image

coding scheme that can achieve excellent compression results via

– partitioning the black regions of the input image into nonoverlapping rectangular regions

– efficiently encoding the locations of the vertices of these rectangles.

Image Partition into RectanglesImage Partition into Rectangles

Binary Image Encoding Matrix R

Encoding Matrix R

using the proposed

approach

Algorithms for PartitioningAlgorithms for Partitioning

• Partition the original image into the minimum number of nonoverlapping rectangles.

• The Optimal Rectangular Partitioning (ORP) algorithm is very slow and has very high complexity.

• A simple and fast Near-optimal Rectangular Partitioning (NRP) algorithm proceeds asfollows:

Algorithms for Partitioning (Cont.)Algorithms for Partitioning (Cont.)1. During the raster (left to right and top to bottom) scan process, when an

unprocessed black pixel is encountered, it is considered as the top left

vertex of a rectangle. The same location in the matrix R should be set to 1

to indicate the existence of a top left vertex of a new rectangle.

2. All the unprocessed black pixels to the right of the above pixel are

included in the new developing rectangle until a terminating, white or

processed black, pixel is encountered. The pixel exactly to the left of the

terminating pixel now represents the top right vertex of the new rectangle.

3. The rectangle then extends downward by including all the unprocessed

black pixels bounded by the column locations of the top left and top right

vertices. The downward extension stops if the following.

a) One, or more, white pixel exists in the new encountered row

within the vertical locations of the left and right vertices of the

rectangle.

b) The new downward row has unprocessed black pixels exactly to the left

and exactly to the right of the left and right vertices, respectively.

Algorithms for Partitioning (Cont.)Algorithms for Partitioning (Cont.)

4. The rightmost pixel in the last row of the developing rectangle is considered as the bottom right vertex of the rectangle. Hence, its location in the matrix R should be set to 2. If the location of the bottom rights vertex is the same as the that of the top left one, then this location in the matrix R should be changed to -1 to indicate the case of a one pixel rectangle.

5. All the pixels in the above rectangle should be indicated as processed black pixels in order not to be processed again. This can be achieved by changing their values in the matrix A to 0 so that they are not to be processed any further.

6. The search of another rectangle resumes from the pixel next to the one identified as the top left vertex of the last encountered rectangle until the

whole image is scanned.

Coordinate Data CompressionCoordinate Data Compression

Matrix R Encoding Bits

11010

0

10011101

01011011001

10000

001010

011000

1001010000

Test Images of different Test Images of different types and sizestypes and sizes

(a) 256x256 (b) 512x512 (c) 379x374

Test Images of different types and sizesTest Images of different types and sizes

(f) 767x572

(d) 346x508

(e) 629x576

Experimental ResultsExperimental Results

Experimental Results (Cont.)Experimental Results (Cont.)

ConclusionConclusion• This paper propose a new binary image coding

scheme that can achieve excellent compression results via – partitioning the black regions of the input

image into nonoverlapping rectangular regions – efficiently encoding the locations of the

vertices of these rectangles.

• The performance of NRP is indeed close to optimal (ORP) while being simpler to implement.

A New Compression Technique A New Compression Technique for Binary Text Imagesfor Binary Text Images

IEEE Symposium on Computers and IEEE Symposium on Computers and Communications (ISCC)Communications (ISCC)

Azhar Quddus and Azhar Quddus and Moustafa M. Fahmy (IEEE Fellow)Moustafa M. Fahmy (IEEE Fellow)

OutlineOutline• Introduction• Image Partition into Overlapping

Rectangles• Algorithm for Partitioning• Coordinate Data Compression• Test Images• Experimental Result• Conclusion

IntroductionIntroduction• This paper propose a new binary image coding

scheme that can achieve excellent compression results via – partitioning the black regions of the input image into

overlapping rectangular regions– efficiently encoding the locations of the vertices of these

rectangles.

• The complexity is justified by the gain obtained in the compression ratio.– Less the numbers of rectangles than nonoverlapping

partitioning – More complex than nonoverlapping partitioning

Image Partition into Image Partition into Overlapping RectanglesOverlapping Rectangles

Nonoverlapping Partitioning Overlapping Partitioning

Algorithms for PartitioningAlgorithms for Partitioning

• Partition the original image into the minimum number of overlapping rectangles.

• Problem:– Partial Overlapping– Conflict

Problem: Partial OverlappingProblem: Partial Overlapping

Situation1:

Problem: Partial OverlappingProblem: Partial Overlapping

Situation2:

Problem: ConflictProblem: Conflict

Partitioning of Image1 Identical Matrix RPartitioning of Image2

Problem: ConflictProblem: Conflict

Conflicting Image Conflicting Image

after Splitting

Matrix R

Coordinate Data CompressionCoordinate Data Compression

Matrix R Encoding Bits

11010

0

10011101

01011011001

10000

001010

011000

1001010000

Test ImagesTest Images

Hindi-English Text (64x64) Arabic-English Text (64x64)

Experimental ResultExperimental Result

ConclusionConclusion• This paper propose a new binary image coding

scheme that can achieve excellent compression results via – partitioning the black regions of the input image into

overlapping rectangular regions– efficiently encoding the locations of the vertices of these

rectangles.

• The complexity is justified by the gain obtained in the compression ratio.– Less the numbers of rectangles than nonoverlapping

partitioning – More complex than nonoverlapping partitioning