Aggregation of Descriptive Regularization and Fuzzy Logic Techniques

for Enhanced Remote Sensing Imaging

A. Castillo Atoche, O. Palma Marrufo and R. Peon Escalante

Facultad de Ingenieria, Universidad Autonoma de Yucatan, M´erida, Mexico

Keywords:

Remote Sensing, Parallel Computing, GPUs.

Abstract:

In this paper, the aggregation of the descriptive regularization and Fuzzy-Logic techniques is proposed for the

enhancement/reconstruction of the power spatial spectrum pattern (SSP) of the wave ﬁeld scattered from re-

motely sensed scenes. In particular, the Weighted Constrain Least Square (WCLS) and the Fuzzy anisotropic

diffusion techniques are algorithmically adapted and implemented in a parallel fashion using commodity

graphic processor units (GPUs) improving the time performance of real-time remote sensing applications.

Experimental results show the performance efﬁciency both in resolution enhancement and in computational

complexity reduction metrics with the presented approach.

1 INTRODUCTION

Advances in sensor technology are revolutionizing

the way of images are collected, managed and pro-

cessed. The incorporation of latest-generation sen-

sors to radar/SAR systems is currently producing

a near-continual stream of high-dimensional image

data. Such amount of collected information is now

required to be processed in (near) real-time mode for

newer applications in Earth monitoring, in medical

image fusion and enhancement, and computer vision.

Relevant examples include monitoring of natural dis-

asters like earthquakes and ﬂoods, military applica-

tions, tracking of man-induced hazards, forest ﬁres,

oil spills and other types of biological agents. Also,

these applications need timely responses for swift

decision which depend upon real-time performance

of algorithm implementation (Henderson and Lewis,

1998),(Chang, 2007), (Goodman et al., 2011), (Yu

et al., 2013). Additionally, the computational com-

plexity of the advanced high-resolution remote sens-

ing (RS) and radar imaging techniques that employ

the recently developed regularization methods for en-

hanced radar imaging and remote sensing (RS) image

reconstruction/ enhancement procedures (Shkvarko

et al., 2008),(Castillo Atoche et al., 2010), (Shkvarko,

2010) is deﬁnitively unacceptable for a (near) real-

time implementation with any existing digital sig-

nal processor (DSP) or high-speed personal computer

(PC). In this regard, a tremendous amount of data pro-

cessing is required to be computed for different type

of image processing algorithms. To provide such high

computational demands under (near) real-time con-

straints, highly parallel processing schemes must be

developed. Usually, general-purposesystems are used

like multi-PC’s, ﬁeld programmable gate arrays (FP-

GAs) or digital signal processing (DSP) platforms.

Therefore, the implementation of the aggregated de-

scriptive regularization and fuzzy anisotropic diffu-

sion techniques via GPU computing for real-time data

processing is considered in this study.

The principal innovation that distinguishes our ap-

proach from previous studies (Paz and Plaza, 2010),

(Castillo Atoche et al., 2009), (Liu and Plaza, 2011)

is twofold: ﬁrst, the conceptualization and algorith-

mically aggregation of the weighted constrained least

square (WCLS) algorithm with the fuzzy Anisotropic

Diffusion technique for image enhancement is em-

ployed. In this stage fuzzy edge detectors are in-

troduced in order to provide a more ﬂexible and ro-

bust way to deﬁne the edges instead of using the

well-known Laplacian ﬁlter as the edge factor in the

anisotropic diffusion. The essential idea is to avoid

blurring of the edges, after the WCLS reconstruc-

tion, with the incorporation of an edge stopping func-

tion which estimates the diffusion coefﬁcients ensur-

ing the smoothing process only in the interior re-

gions without crossing the edges. Second, the al-

gorithmic implementation using massively processors

with a graphic processing unit (GPU) platform is per-

formed. Here, parallel computing techniques are used

in order to improve the time performance of the algo-

193

Castillo Atoche A., Palma Marrufo O. and Peon Escalante R..

Aggregation of Descriptive Regularization and Fuzzy Logic Techniques for Enhanced Remote Sensing Imaging.

DOI: 10.5220/0005154301930198

In Proceedings of the International Conference on Fuzzy Computation Theory and Applications (FCTA-2014), pages 193-198

ISBN: 978-989-758-053-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

rithm. Simulation analysis and the performance eval-

uation with the NVIDIA Tesla C2075, are indicative

that our GPU-based implementation is also oriented

toward real-time remote sensing processing applica-

tions.

2 PROBLEM STATEMENT

In radar imaging (Henderson and Lewis, 1998), (Shk-

varko et al., 2008), the backscattered ﬁeld of the re-

motely sensed surface X ∋ x is modeled by impos-

ing its time invariant complex scattering function e(x)

over the object scene X ∋ x. The measurement data

waveﬁeld u(y) = s(y) + n(y) consists of echo signals

s and additive noise n, and is available for observa-

tions and recordings within the prescribed time-space

observation domain Y = T ×P, where y = (t,p)

de-

ﬁnes the time-space points in Y. The model of the

observation waveﬁeld u is deﬁned by specifying the

stochastic equation of observation (EO) of an opera-

tor form: u = Se + n;e ∈ E;u,n ∈ U;S : E → U, in

the Gilbert signal spaces E and U with the metric

structures induced by the inner products [u

]

and

]

, respectively.

All the ﬁelds e,n,u are assumed to be zero-mean

complex valued Gaussian random ﬁelds. An incoher-

ent nature of the backscattered ﬁeld e(x) is next as-

sumed, this is naturally inherent to the radar imaging

experiments (Henderson and Lewis, 1998), (Shkvarko

et al., 2008) and leads to the δ-form of the object ﬁeld

correlation function, R

) = B(x

)δ(x

− x

where e(x) and B(x) =< |e(x)|

> are referred to as

a random complex scattering function of the probing

surface and its average power scattering function or

spatial spectrum pattern (SSP), respectively.

Next, the conventional ﬁnite-dimensional vector

form approximation (Castillo Atoche et al., 2010) of

the continuous-form EO is taked into account as fol-

lows

u = Se+ n (1)

where u,n and e deﬁne the vectors composed by

the coefﬁcients of the ﬁnite-dimensional approxi-

mation of the ﬁelds u,n and e, respectively, and

S is the matrix-form approximation of the sig-

nal formation operator (SFO). The average b =

vect



< e

∗

>;k = 1,...,K



of the random scatter-

ing vector e has a statistical meaning of the average

power scattering function traditionally referred as the

spatial spectrum pattern (SSP), where the asterisk in-

dicates the complex conjugate. This SSP is a second

order statistics of the scattered ﬁeld that represent the

brightness reﬂectivity of the image scene B = L{b},

represented in a conventional pixel format over the

rectangular scene frame (Shkvarko et al., 2008).

The RS imaging problem is stated as follows: to

ﬁnd an estimate of the scene pixel-frame image

via lexicographical reordering

B =L{

b} of the spa-

tial spectrum pattern (SSP) vector estimate

b recon-

structed from whatever available measurements of

independent realizations {u

( j)

; j = 1,.. .,J} of the

recorded data vector.

3 DESCRIPTIVE

REGULARIZATION STRATEGY

In this section, vector

b is estimated as a discrete-

form representation of the desired SSP over the pixel-

formatted object scene remotely sensed with an em-

ployed array radar/SAR. Thus, one can seek to esti-

mate

b = {

}

diag

given the data correlation matrix

pre-estimated by some means, e.g. via averaging

the correlations over L independent snapshots (Shk-

varko, 2010), (Castillo Atoche et al., 2009);

= Y

= (1/L)

∑

l=1

(l)

, and by determining the solution

operator that we also refer to as the signal image for-

mation operator (SO) W such that

b = {

}

diag

= {WYW

}

diag

. (2)

To optimize the search of W, the following de-

scriptive regularization strategy is proposed

W −→

min

{ℜ(W)} (3)

where

ℜ(W) = tr{(WS− I)A(WS− I)

} +

αtr{WR

} (4)

implies the minimization of a weighted sum of the

systematic and ﬂuctuation errors in the desired esti-

mate

b, where the selection (adjustment) of the regu-

larization parameter α and the weight matrix A pro-

vides the additional degrees of freedom incorporating

any descriptive properties of a solution if those are

known a priori (Shkvarko et al., 2008).

Solving the minimization problem of (3), we ob-

tain

W = K

A,α

−1

, (5)

where

A,α

= (S

−1

S+ αA

−1

)

−1

(6)

and the desired SSP estimate is given by

b = {K

A,α

−1

A,α

}

diag

. (7)

In the case of white noise, R

−1

= (1/N

)I is consid-

ered. Thus, for the case of the proposed weighted

FCTA2014-InternationalConferenceonFuzzyComputationTheoryandApplications

194

constrained least square (WCLS) algorithm, a mod-

iﬁed version of (7) is determined. The following re-

adjustments of the degrees of freedom are employed

A = M

and α = N

. Therefore, the WCLS esti-

mator is represented as follows

WCLS

= (S

−1

S+ αM

)

−1

. (8)

Any other feasible adjustments in the degrees of free-

dom (the regularization parameter α, and the weight

matrix A) provide other possible SSP reconstruction

techniques that are not considered in this study.

4 AGGREGATION OF FUZZY

ANISOTROPIC DIFFUSION

TECHNIQUE

In this section, the aggregation of fuzzy anisotropic

diffusion technique is incorporated for the enhaced of

remote sensing imaging. First, the diffusion process-

ing technique is considered as the result of convolv-

ing the reconstructed remotely sensed image

with

a Gaussian kernel G of increasing width as follows

b(x,y,t) =

(x,y) ∗ G(x,y,t). (9)

Here, (9) acts as a low-pass ﬁlter suppressing high fre-

quencies in the image

b. The problem is that the im-

age edges and noises are both high frequency signals,

and therefore, the edges are blurred by this operation.

To solve this problem, the anisotropic diffusion equa-

tion proposed in (Song and Tizhoosh, 2003) is next

deﬁned as

∂

(r;t)

∂t

= div(c(r;t)∇

b(r;t)), (10)

where R ∋ r = (x,y) for the continuous 2-D rectan-

gular scene frame, c(r;t) = g(



∇

b(r;t)



) is the dif-

fusion coefﬁcient where g(·) is called edge stopping

function, ∇

b is the gradient of the image and

∂

(r;t)

∂t

represents the enhanced SSP estimate

b(r;t) which

provides edge preservation in the scene regions with

high gradient contrast while performing smoothed

windowing over the homogeneous image zones cor-

rupted by Gaussian noise.

Now, the discrete version of the anisotropic diffu-

sion equation of (10) is represented as

[i+1]

[i]

+ λ



· c

· D

(

b) +

· c

· D

(

b)+

· c

· D

(

b) +

· c

· D

(

b) +

· c

· D

(

b) +

· c

· D

(

b) +

· c

· D

(

b) +

· c

· D

(



[i]

(11)

where c

, c

represents

the conduction coefﬁcients, d

are the distance

between pixels and D

, D

indicates the nearest-neighbour differences for

the corresponding direction.

In this paper, the conduction coefﬁcients are cal-

culated as follows





. (12)

The parameter K in (12) is chosen according to the

noise level and the edge strength. In any remote

sensing system, the noise level is not known a priori

with certainty (Henderson and Lewis, 1998). Further-

more, because of inherent noise, the calculated edge

strength based on gradient is not a true reﬂection of

the edge strength. Therefore, the ambiguity of choos-

ing a suitable value for parameter K, and thus, the un-

certainty in the diffusion coefﬁcient justiﬁes the use

of fuzzy set theory in such situations.

In this regard, each nearest-neighbor differences

, that deﬁne the edge factor algorithmically same

as Laplacian Filter in each direction in the traditional

Perona-Malik anisotropic diffussion algorithm, is re-

placed by a Fuzzy Logic Set (FLS) that calculates the

edges in order to avoid the noise of the remote sensing

images. The following fuzzy rules are deﬁned

The proposed fuzzy anisotropic diffusion ap-

proach is next deﬁned as

[i+1]

[i]

+ λ



· c

· ϒ

(

b) +

· c

· ϒ

(

b)+

· c

· ϒ

(

b) +

· c

· ϒ

(

b) +

· c

· ϒ

(

b) +

· c

· ϒ

(

b) +

· c

· ϒ

(

b) +

· c

· ϒ

(



[i]

(13)

where ϒ

represents the edge in each direction using

a centroid deffuziﬁer. Now, the design is ready to im-

plement the Fuzzy Anisotrpic Diffusion in the GPU

platform.

AggregationofDescriptiveRegularizationandFuzzyLogicTechniquesforEnhancedRemoteSensingImaging

195

Table 1: Proposed Fuzzy rules.

and

}

are Zero

then

{Black}

Else

{White},

and

}

are Zero

then

{Black}

Else

{White},

and

}

are Zero

then

{Black}

Else

{White},

and

}

are Zero

then

{Black}

Else

{White},

and

}

are Zero

then

{Black}

Else

{White},

and

}

are Zero

then

{Black}

Else

{White},

and

}

are Zero

then

{Black}

Else

{White},

and

}

are Zero

then

{Black}

Else

{White}.

5 GPU IMPLEMENTATION

In this section, the GPU-based implementation of the

aggregated WCLS-Fuzzy anisotropic diffusion algo-

rithm is developed. Figure 1 illustrates the ﬂowchart

of the proposed system describing the methodology

for enhancement of remote sensing imaging. The

multicore architecture of the GPU and the employe-

ment of textures memories for high-speedaccess were

taked into account in the design. In this study, CUDA

kernels were used, which are subroutines callable

from the host that execute on the CUDA device. That

is, an extern function is called from the host and it

calls the different kernels. A kernel employ many

threads to perform the speciﬁc operation deﬁned in

the kernel source code. Moreover, the kernel should

make partitions of the data to be processed by each

thread, taking care of not overlap threads processing

on any memory section in order to avoid undesired

Figure 1: Flowchart describing the methodology adopted

for the development of the system.

results. Three different types of data partitioning are

identiﬁed for image processing: spectral, spatial and

mixed, as illustrated in Figure 1. Considering the

analysis of the previous WCLS and Fuzzy anisotropic

diffusion algoritms, the spatial partition is selected in

order to improve the parallelism in the design.

Now, the computational procedures for the imple-

mentation of the WCLS reconstructive algorithms are

described. First, the device overlap function was ac-

tivated with the capacity to simultaneously execute a

CUDA kernel while performing a copy between CPU

to GPU memory (Sanders and Kandrot, 2011). Mul-

tiple CUDA streams are created to perform this over-

lap of computation in data transfer. In addition, the

memory conﬁguration management using the mmap

library of GNU C is employed. Second, the matrix

operations of the WCLS algorithm are computed. A

speciﬁc CUDA kernel is implemented using one grid

of n× m blocks, in which each block process the cor-

responding sub-matrix operation in a parallel scheme,

and the results are loaded in the shared memory of

the GPU. The reduction algorithm is proposed for the

implementation of several addition operations in this

stage.

For the aggregation of the Fuzzy anisotropic dif-

fusion, a triangular membership function deﬁne the

fuzzy sets. The Fuzzy sets are initialized using the tri-

angular membership function with the following val-

ues, White = 147, Black = 107 and Zero = 5. These

Fuzzy sets are allocated in the GPU memory, and the

use of NPP library is considered, which optimize the

functions that work on 1-D and 2-D arrays.

Next, the extern function PeronaMalik is called

from host, it binds the texture to array, calls the Fuzzy

kernel for image enhancenment and normalize the

resulting array using optimized Nvidia Performace

Primitives, i,e., the nppsMinMax32f to get the min-

imum and maximum ﬂoat value resulting form the

Fuzzy kernel, and nppsNormalize32f to normalize the

image with resulting minimum value at 0 and maxi-

mum at 255.

Summarizing, each thread apply the fuzzy rules,

deffuziﬁes the fuzzy set and compute the values for

the fuzzy anisotropic diffusion. The fuzzy rules are

implemented in the form of minimum function for the

conditional part of the rule. The fuzzy sets Black and

White are implemented also as minimum functions.

Figure 2: Types of image data partitioning: (a) spectral, (b)

spatial and (c) mixed.

FCTA2014-InternationalConferenceonFuzzyComputationTheoryandApplications

196

Afterwards, the fuzzy sets are defuzziﬁed computing

the centroid of them. Finally, the resulting scalar is

used on the fuzzy anisotropic diffusion equations.

6 SIMULATIONS AND

PERFORMANCE ANALYSIS

In order to demonstrate the image enhancement with

the proposed approach towards real-time processing,

the following simulation experiments are conducted

using a real-world satellite image. The tested scene

is shown in Fig. 3(a). In the reported simulations,

the case of white observation noise (Henderson and

Lewis, 1998) is considered with SNR of 20 dB as

shown in Fig. 3(b). Fig. 3(c) presents the image en-

hancement using the Perona-Malik anisotropic diffu-

sion method and Fig. 3(d) shows the image enhance-

ment with the proposed WCLS-fuzzy anisotropic dif-

fusion method.

In the presented performance analysis, the pro-

posed algorithm was implemented in the CPU quad

core Intel Xeon E5603 at 1.6 GHz and in the NVIDIA

Tesla C2075 GPU plattform as well. The results of

such comparative analysis are shown in Table 1.

Table 2: Processing time comparative.

Image size (pixels)

Time processing (seconds)

CPU GPU

512 x 512

1024 x 1024

14.83 0.95

43.24

1.75

In this regard, the time performance of the pro-

posed algorithm againts the C++ reference implemen-

tation have been compared.

Having analyzed Table 1, it is possible to note

that the processing time required for the WCLS-fuzzy

anisotropic diffusion algorithm implementation has

been signiﬁcatively reduced using GPUs. Such GPU

implementation requires 1.75 sec for a 1024 x 1024

pixel-format image instead of the 43.24 secs required

using the C++ implementation.

Then, the processing time of the proposed GPU

based algorithm is about 27 times less than the con-

ventional CPU implementation.

7 CONCLUSIONS

The principal result of this study relates to the

GPU-based implementation of the aggregated deter-

ministic regularization and Fuzzy-Logic techniques

oriented for high-resolution enhanced of remotely

sensed imaging. We have examined that pursuing

(a)

(b)

(c)

(d)

Figure 3: Implementation results: (a) original real-world

test scene; (b) degraded scene image formed applying the

Matched Space Filter method; (c) image reconstructed ap-

plying the WCLS algorithm (4.57 dB); (d) image ehanced

applying the WCLS-Fuzzy Anisotropic Diffusion algorithm

(9.76 dB).

AggregationofDescriptiveRegularizationandFuzzyLogicTechniquesforEnhancedRemoteSensingImaging

197

the proposed GPU computing implementation, the

sub-tasks of the WCLS and the Fuzzy-Anisotropic

diffusion algorithms can be algorithmically properly

adapted in computationally efﬁcient parallel represen-

tation towards real-time remote sensing applications.

The efﬁciency of the GPU-based implementation ap-

proach was veriﬁed with a real test-case scenario in

which the time performance of the algorithm was sub-

stantially reduced up to 27 orders.

ACKNOWLEDGEMENTS

This study was supported by Programa de Mejo-

ramiento del Profesorado (PROMEP) and Consejo

Nacional de Ciencia y Tecnolog´ıa (CONACYT) un-

der grants UADY-CA-84 and CB-2010-01-158136,

respectively. The authors wish to thank Eduardo Es-

cobar Aquino for his support in running the proposed

experiments.

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