Efficient Variable Size Template Matching Using Fast Normalized Cross Correlation on Multicore Processors

“Efficient Variable Size Template Matching
Using Fast Normalized Cross Correlation on
Multicore Processors”
Durgaprasad Gangodkar, Sachin Gupta, Gurbinder Gill,
Padam Kumar, Ankush Mittal

Department of Electronics and Computer Engineering
INDIAN INSTITUTE OF TECHNOLOGY
Roorkee
India
1

Contents
1. Introduction

2. NVIDIA’s Compute Unified Device Architecture

3. Normalized and Fast Normalized Cross Correlation
4. Parallel Implementation of Fast Normalized Cross
Correlation

5. Experimental Details and Performance Evaluation

6. Conclusion
2

1. Introduction
Template Matching has its applications in image and signal
processing like image registration, object detection, pattern
matching etc. Given a source image and a template, the
matching algorithm finds the location of template within the
image in terms of specific measures.
• Full search (FS) or exhaustive search algorithms consider
every pixel in the block to find out the best match --
computationally very expensive.
• Though there are different measures proposed. An empirical
study found NCC provides the best performance in all image
categories in the presence of various image distortions [9].
NCC is also more robust against image variations such as
illumination changes then widely used SAD and MAD .
3

• However NCC is computationally very expensive
than SAD or MAD, which is a significant drawback in
its real-time application.

• In this paper we propose the parallel
implementation of template matching using Full
Search using NCC as a measure using the concept of
pre-computed sum-tables [10][11] referred to as
FNCC for high resolution images on NVIDIA’s
Graphics Processing Units (GP-GPU’s)

4

2. NVIDIA’s Compute Unified Device Architecture
• GP-GPUs have emerged as front runners for low-cost
high-performance computing (HPC) machines
• GTX280 can provide theoretical peak performance of
around 933 GFLOPs (single precision) and 78 GFLOPs
(double precision).
• A kernel executes a scalar sequential program on a set of
parallel threads. The programmer organizes these threads
into a grid of thread blocks.
Challenges:
• Higher global memory latency
• Higher CPU – Device data transfer latency
• Limited availability of registers
• Limited high-speed shared memory
• Thread synchronization and dynamic kernel configuration
5

Main contributions of this paper:
1. Novel strategy for parallel calculation of sum-tables using
prefix-sum algorithm that optimally uses high-speed shared
memory of GPU.
2. Adaptation of the kernel configuration to variable sized
templates and efficient use of shared memories offered by
CUDA
3. Exploitation of the asynchronous nature of kernel calls to
optimally distribute computation between host and device.
4. Data parallelism in the algorithms by dividing
computationally intensive tasks for parallel and scalable
execution on the multiple cores.

6

3. Normalized and Fast Normalized Cross Correlation
• NCC has been commonly used as a metric to evaluate the
similarity (or dissimilarity) measure between two
compared images[8][9].
• Template of size ܰ‫ ݕܰ × ݔ‬is matched with an image of
size ‫.ݕܯ × ݔܯ‬
• The position (‫)ݏ݋݌ݒ , ݏ݋݌ݑ‬of the template ‫ ݐ‬in image ݂ is
determined by calculating the NCC value at every step.
• The basic equation for NCC is as given in (1)

∑ ( f ( x, y) − fu,v )(t( x − u, y − v) − t )
γ u,v = x, y
(1)
∑
x, y
( f ( x, y) − f u,v ) 2
∑
x, y
(t( x − u, y − v) −t ) 2

7

u+N −1 v + N −1
1 x y

f u ,v = ∑ ∑ f (x, y) (2)
N xN y x=u y=v

• Direct computation of (1) involves the order of
ܰ‫ ) ݕܰ − ݕܯ() ݔܰ − ݔܯ( ݕܰ × ݔ‬calculations.
• For example, to match a small 16×16 pixel template
with a 250×250 pixel image would require a total of
more than “14 million calculations”

8

Fast Normalized Cross Correlation (FNCC)
• Calculation of the denominator of equation using the
concept of sum-tables[10][11].
• ‫ݒ ,ݑ(ݏ‬ሻ ܽ݊݀ ‫2ݏ‬ሺ‫ݒ ,ݑ‬ሻ are sum tables over image
function and image energy respectively.
• The sum-tables of image function and image energy
are computed recursively as given below:
(1)

(2)

(3)

(4)
9

4. Parallel Implementation of Template
Matching
• Though FNCC reduces computational time for low
resolution images, incurs substantial time for high
resolution images.
• We adopt two stage approach for template matching
– In the first stage we parallelize the computation of the
sum-tables
– In the second stage we parallelize the computation of
normalized cross correlation by utilizing the sum-tables
as a look up.

10

Computation of Sum-Tables
• The sum tables are calculated by taking the cumulative sum
over the image points.
• We make use of parallel prefix-sum algorithm as shown in
figure

The figure illustrates the working of prefix sum algorithm,
where n/2 threads can work in parallel to calculate prefix sum
in O(logn) time complexity
11

• Sum-tables for template on the host CPU, while GPU is busy
calculating the sum-tables for the source image exploiting
asynchronous nature of kernel calls. This eliminates idling of
host CPU when device is busy
• One row to a thread block.
• Task of each thread grouped in a block configuration
dynamically decided by template size.
• Every thread caches data in shared memory for template
image of variable resolution.
• Parallel prefix-sum transpose Parallel prefix-sum
transpose sum-table
• Use of device pointers in total of four kernels to avoid data
transfer latencies.
12

Template matching using FNCC
• For a template of size ܰ௫ × ܰ௬ pixels we divide the source
image into search window of 2ܰ௫ × 2ܰ௬ pixels.
• The correlation value is calculated utilizing the sum-tables
as lookup by moving the template over the referenced
search window pixel by pixel, covering the entire search
window.

• Highest Correlation indicates best match
• The task of computing correlation for each search window
is assigned to a single thread. 13

• The target image is dynamically divided into search
windows according to the x and y dimensions of the
variable sized template such that we get the maximum
number of threads per block.
• Every thread block dynamically caches data such that
constraint of shared memory (16 KB per block ) is never
violated.
14

5. Experimental Details and Performance
Evaluation
• Execution time and speedup of proposed parallel
implementation FCC algorithm evaluated on benchmark
dataset .
• Sequential code implemented on Intel Xeon 3.2 GHz
processor with 1 GB of DRAM and 32 bit Windows XP OS.
• Parallel code was implemented on NVIDIA GTX 280 having
1 GB of DDR3 onboard Intel Xeon 3.2 GHz processor with 1
GB of DRAM and 32 bit Windows XP OS.

15

CUDA
Image Size in Template Sequential
Size in Thread Threads Execution Time in sec. Speedup
pixels pixels Blocks Per Block Time in
sec.
512x512 32x32 5x8 3x2 0.517 1.372 2.7
24x32 8x5 2x5 0.260 1.097 4.3
24x16 5x6 6x4 0.047 0.543 11.6
16x16 5x6 7x6 0.033 0.406 12.3
1024x1024 32x32 9x16 3x2 1.311 6.170 4.8
24x32 16x9 2x5 0.639 4.773 7.5
24x16 10x11 6x4 0.179 2.518 14.1
16x16 10x11 7x6 0.121 1.893 15.6
2048x1080 32x32 10x32 3x2 2.848 13.474 4.8
24x32 17x17 2x5 1.261 10.344 8.3
24x16 11x22 6x4 0.391 5.551 14.3
16x16 10x22 7x6 0.239 4.116 17.3

• For frame size of 2048x1080 and template size 16x16 we could
achieve the considerable reduction in execution time from 4.116 sec
to 239 ms yielding a speedup of around 17x.
16

• As the resolution of the image increases the speed-up
obtained also increases hence opening up the scope for
handling high resolution digital images.

17

6. Conclusion
• Every thread has been assigned an independent task of
computing the correlation for template which eliminates
inter-thread communication, inter-thread dependencies and
synchronization.
• Dynamic arrangement of threads into blocks and grids has
been done depending on the size of the template.
• We have also devised efficient strategy to make use of the
faster shared memory to overcome memory access latency.
• Thread configuration is scalable to match low resolution or
high resolution images and varying size template.
• Our future work involves exploring division of larger
templates into smaller sub-templates further exploit the
computational power of multicore processors 18

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10. Briechl K., Hanebeck, U. D.: Template Matching Using Fast Normalized Cross Correlation. In: SPIE,
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Efficient Variable Size Template Matching Using Fast Normalized Cross Correlation on Multicore Processors

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