Towards Low Partition Overhead in Image Decomposition SCI (2003) Ju - - PowerPoint PPT Presentation

Towards Low Partition Overhead in Image Decomposition

SCI (2003)

Ju Wang, University of Florida

Motivation and Goals

• Image decomposition is required in parallelizing many image processing

algorithm

• Different decomposition solutions can affect the performance gain of the

parallelism

• Decomposition scheme determines the additional overhead associated

with inter-processor communication, due to – Local dependency of image pixels – Communication delay in cluster and distributed memory systems

• This overhead should be minimized, especially for real-time image

(video) processing, such as parallelized video encoding.

• Goal: develop image decomposition algorithms that result in

low partition overhead, and demonstrate one particular application in MPEG-2 video decoding.

Model of the Parallelized Image Algorithm

• The image processing algorithms considered here are decomposable
• Parallel processing is achieved by executing multiple identical threads
• Each thread works on an assigned area of the original image
• There is no dependancy among parallel threads
• The results of individual threads are merged in a master node

Image Decomposition Problem Description Notations:

• pixel set I : the set of all pixels for a rectangle-shape image with width w

and height h

• local dependency f : I −

→ 2I, which maps a pixel in I to a subset of I. f is determined by a specific image processing algorithm

• {P1, P2, ..., PN} be a N-way disjoint partition for image I where Pk ⊂ I is

the kth part

Definition of Decomposition Overhead

PO(P, N, f) =

• k=1...N
• i∈Pk

{j ∈ f(i) and not j ∈ Pk}

Determining Communication Overhead

The amount of additional image data need to be accessed by other processing threads is determined by

• the pattern of local dependence determined by the image processing

algorithm. – In image smoothing filter, the size of the kernel mask determines the neighborhood surrounding the target pixel.

• the partition method used.

A good partition can limit the partition

• verhead within a reasonable range.

While a ill-partitioned image might require the access of the whole image in each threads. Such a bad partition can be constructed by zig-zag scanning the image, and assigning pixels to different threads in round-robin.

Decomposition Overhead Example

A B C D

• Total length of internal partition edge
• Diameter of neighboring area
• Problem reduced to the search of partition with the shortest partition

circumference

More Partition Examples

A B C D (b) (a) A B C D A D B C B A D C (c) (d)

More Partition Examples

A B C D B C (a) another 4−piece−partition (b)the reference area of piece A A D

Low Boundary Analysis

Fact: for a given area, the shape with the shortest circumference is circle. Assume that the image is a perfect square with edge length w,

• the image is to be divided into N disjoint piece with equal area, the area
• f each part must be w2/N.
• the radius of the circles in the ideal partition is r =
• w2/N ∗ π.
• partition must be the optimal one with shortest overall circumference.
• the circumference for each circle: c = 2 ∗ π ∗ r = 2 ∗
• π ∗ w2/N.
• The total circumference of the N circles become Tc = N ∗ c = 2 ∗

√ π ∗ N ∗ w2 = 2 ∗ w ∗ √ π ∗ N.

• subtract the external circumference of the original image, which is 4 ∗ w
• ci(w, N) = Tc−ce

2

= w ∗ √ π ∗ N − 2 ∗ w

Horizontal-Vertical Partition and Low Boundary Results

10 20 30 40 50 60 70 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 −*−pseudo ideal partition −o−HV partition

• Partition overhead grows as the number of partition increases.
• H-V partition is comparable to ideal partition at small scale parallel setting.

Problem Formulation

• quadric assignment problem :

min(

• i,j∈{1···N}
• k,h∈{1···K}

Xi,k.Xj,h.dk,h.ri,j)

• Xi,j = 1 when macroblock i is assigned to jth processor.
• Xi,j ∈ {0, 1},

i Xi,j = H·V K

j Xi,j = 1

Heuristic Partition Algorithm

• divide and conquer
• image area is divided into two parts each time
• always try the shortest dimension when dividing a image part
• the division is balanced in determine the area of sub image area

Partition Example with Proposed Heuristic Algorithm

partition(r2,3) partition(r1,4) partition(r3,2) partition(r4,2) partition(r5,2) partition(r0,7)

Performance Results

5 10 15 20 25 30 35 40 5 10 15 20 25 30 35

Number of Partition Amount of Reference Data per Picture (Mbits) −.− Horizontal partition −*−vertical partition −+−HV partition −d−Quick partition Search Window Size=32 pixels Picture size: 720*480 Reference Data In Data Partition Algorithms

Conclusion

• Discussed the challenge of image decomposition in parallel image

processing

• provided an analysis for the low boundary of partition overhead
• Proposed an heuristic algorithm which can produce good partitions with

low decomposition overhead

• Our experiments of this algorithm in a parallel MPEG-2 video decoder

shows positive preliminary results.

Thank You!