Change Detection using undecimated Wavelet Transform Fusion and Genetic Algorithm

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 8, Issue 1, January 2018)

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Change Detection using undecimated Wavelet Transform

Fusion and Genetic Algorithm

Josephina Paul

1

KCAET, Tavanur, Kerala Agricultural University, India

Abstract— Change detection using remote sensing images

have great significance in this information age, since it has diverse applications such as urbanization study, protection of

nature, monitoring land use changes and disaster

management. In this paper, an algorithm to enhance the information contents, two input images have been fused in the UDWT domain and further, these coefficients are segmented by a genetic algorithm to label the changed and unchanged pixels to generate the change map. The efficacy of the method was evaluated by qualitative as well as quantitative accuracy metrics and found to be performing superior to individual methods. The results of the two data sets chosen demonstrate the suitability of the proposed technique in the urbanization and the land use changes studies.

Keywords— Undecimated Wavelet Transform, fusion, Genetic Algorithm, change detection, remote sensing.

I. INTRODUCTION

Change detection using images has gained enormous attraction in the recent decades due to its wide array of applications in various fields. It involves medical diagnosis[1], detecting alteration in geography[2] caused by natural phenomena or human interventions and diverse industrial applications. Due to the leap in space technology, a huge volume of remote sensing images are piling up every day, which can be utilized for various studies such as urbanization, protection of nature and wild life, land use changes, disaster management etc [2]. Multispectral satellite images contain multiple spectral bands carrying details of various land cover objects as the onboard MSS operates at different range of spectral radiation and therefore, these images are more suitable for the remote sensing change detection analysis. In order to evaluate the changes, it requires two co-registered images [3] of the same scene acquired at two time points. In literature, change detection involves three major steps[2-3]. Firstly, the images are pre-processed for rectifying errors trapped in, due to various environmental conditions while capturing. The images are to be registered on the same co-ordinates which is also called geo-referencing, to align them into the same latitude-longitude measures.

Next, from the pre-processed, co-registered images, the difference image is generated by employing various methods such as rationing and subtraction. The logarithmic operation is often applied on rationing, as it is efficient in handling different noise models. Since the range of variation in the signals gets reduced on logarithmic scale, the weak signals get enhanced as well [2]. Finally, the difference image is grouped into two using various methods such as thresholding or by a segmentation algorithm. However, from the literature, it is evident that the whole performance and quality of the change map largely depends upon the quality of the difference image and the segmentation algorithm[3]. Several attempts can be seen in literature to improve the quality of difference image as well as the quality of the change map. One popular and much explored technique is fusion[2-5]. In [3] a fusion technique was employed in the discrete wavelet transform (DWT) domain to enhance the quality of the difference image and thereby the accuracy of the change detection map in combination with a fuzzy clustering algorithm for labeling the changed and unchanged pixels. A bunch of fuzzy variants and hybrid algorithms have been used in [6], to find the geographical changes occurred. Support vector machine based algorithms have been attempted in [7]. In [8] minimization of a cost function using genetic algorithm was employed to generate a good quality change map. Thresholding [9-11] is often used to delineate the changed and unchanged pixels, but, the choice of a proper threshold has always been a problem[10]. In this paper, we are addressing the two issues mentioned above, with the help of Undecimated Wavelet Transform (UDWT) [12] and genetic algorithm[8] due to their multiple properties as detailed in section 2.

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II. METHODOLOGY

A. Wavelets

Wavelets are functions that can represent a signal into various frequency components. In addition to that it can transform the signal into multiple scales also. As the image is a two dimensional signal, wavelets can be used for analyzing images at multiple coarseness and frequencies.

Mathematically, a wavelet is a function with zero average, represented as

(1)

A wavelet transform of a function 𝒇 ∊ L2 at time 𝞃 and scale s can be written as

W(𝒇(𝞃,s))= (2)

An inverse wavelet function can be applied to the transform and the function (image) can be reconstructed. In wavelet, the limitation of Fourier transform is overcome by incorporating the time domain along with the frequency information of the signal. ie. the FFT can represent the signal in terms of frequency only, but the time at which it occurs, cannot be answered by the FFT. Whereas in wavelet, the temporal information pertaining to a signal also can be represented in addition to its capability of representing frequencies at multi scales. Moreover, various frequency bands can be clearly delineated which help analyze the image in multiple coarseness. The spatial as well as temporal information is retained even after the decomposition of the signals, and its ability to represent at multiple coarseness, the essential property required to analyze images in detail make this transform suitable for the research on change detection of remote sensing images [5,13]. Since its advent, several families of wavelets have been developed and are popular in signal processing. We have used undecimated discrete wavelet as they preserve the scale of the source images on decomposition into sub bands, unlike discrete wavelets which reduce the sub band image size into half on every level of decomposition.

The UDWT decomposes the image into one low frequency sub band and three high frequency sub bands, horizontal, vertical and diagonal directions, denoted as LL, LH, HL and HH respectively.. On successive decomposition of LL, it again decomposes into 4 sub bands as earlier thus creates 3J+1 redundancy at Jth level.

B. Genetic Algorithm

Genetic algorithms are search algorithms that mimic the theory of evolution-‘survival of the fittest’.

It is a probabilistic optimization method [14-15] anchored to various evolutionary phenomena such as natural selection, cross over and mutation. When the search space is vast, sub-optimal solutions can be drawn randomly from it and form a population of candidate solutions. The individuals of the population, also called chromosomes, are again trying to find better solutions iteratively, undergoing natural processes as mentioned, and finally, the fittest one is evolved that carries a global or nearly global solution. A fitness function[15] is employed on each iteration, to evaluate the quality of fitness that determines where and when to stop the search. GA is robust in landing on optimum solutions from a large search space continuously reforming itself towards the intending goal. Therefore, genetic algorithms can be applied to any optimization problems and thus, to the clustering problems too.

Unlike the gradient method or other conventional search algorithms, the GA has several alternate solutions at hand and they compete each other to come up with a global best solution by evolving themselves towards it. At the same time, they discard the ones which are not fit enough /or fail to produce the global solution. This is achieved by various genetic operations employed on the population as detailed below.

(i) Selection

This is a process of selecting individuals or chromosomes from the population so as to ensure only potential individuals are moved on to the next generation based on the fitness value. Two common methods adopted are (i) deterministic, where only the individuals with highest fitness value is selected and (ii) random, where the selection is based on probability. The individuals with higher fitness value will have higher probability to be selected. The method often used is a roulette wheel selection where each roulette wheel portion indicates a weight proportional to the fitness of individuals, and it is spun to choose the individual. The following formula is applied for this

Probability of i being selected = (3)

Where fi is the fitness of ith individual and n is the size of population. When it is a minimization problem, the inverse of the fitness is taken to assign the weight of the individual in a Roulette wheel.

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In tournament selection several tournaments are played among a few individuals. The individuals are chosen at random from the population. The winner of each tournament is selected for next generation. Weak individuals have a smaller chance to be selected if the tournament size is large.

In Rank selection the chromosomes with highest ranked fitness values are selected and the rest is discarded. Whereas in steady state selection, a number of good chromosomes are moved to the next generation and some bad chromosomes are replaced by the chosen best ones. All other individuals are moved to the next generation.

Algorithm 1: Genetic Algorithm

1. Generate the initial random population size n, from the dataset

2. Evaluate the fitness of each individual according to a fitness function.

3. Repeat until required population size is reached for next generation

3.1. Select the fittest individual pairs for mating. 3.2. Apply reproductive operator crossover. The cross over point is determined and swap to create offspring.

3.3 With a probability, mutate the selected parents –mutation operator

3.4 Move the best parents to the next generation (Elitism)

4. Evaluate the fitness of the individuals of the next generation (generated in the step 3)

5. Stop if stopping criterion is met, else go to step 3.

(ii) Cross Over

Cross over is the process of exchanging two or more genes between the chromosomes. In nature, it results often in generating better offspring carrying traits of both the parents. Similarly, in GA , two chromosomes of better fitness are crossed by swapping a few genes selected randomly. Cross over can be one point crossover or multipoint. While the former chooses a single position in the chromosome randomly and swaps the two tails, the latter has cross over position at multiple positions and are implemented by different methods. Among them, N-point cross over, segmented cross over, uniform cross over and shuffled cross over are the popular methods [15].

(iii) Mutation

In reality, mutation is the aberration of genes in the chromosome that arises randomly by external agents or by the abnormal behavior of the system itself.

In GA, mutation is the process of introducing new genes (features) into the chromosomes to maintain the diversity of population. Mutation can be applied on a single gene (point) or at multiple points or as a whole to a chromosome. According to a probability value, a random position is selected and the mutation is applied. In binary coded string, inversion of a single bit or more than one bit can be done. If rand[0,1]>Pi, where Pi is the probability, mutation is done. To avoid any chaotic effect the value of probability value is kept at low.

Elitism

There are chances to destroy the best solutions by applying selection or mutation. A different approach in genetic operation is the Elitism [15] in which the best chromosomes are preserved in the population and moved to the next generation. Elitism is defined in terms of percentage or number.

Representation

The chromosomes are usually coded into binary valued strings or real-valued, depending on the problem at hand. In binary, the chromosomes are represented as a d-dimensional string of 0’s and 1’s in the encoded form of data In real valued, the data is directly represented in a d-dimensional chromosome.

III. THE PROPOSED CHANGE DETECTION TECHNIQUE

The bi-temporal images at time t1 and t2 are first pre-processed for radiometric correction and geo-referenced to co-register with the same co-ordinates. Since we are using a fusion technique, it is used a mean ratio image and a log ratio image which are generated as

(4)

(5)

Where is mean ratio image, and are the local

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The two difference images-mean ratio image and log ratio image –were decomposed by UDWT upto two levels and generated one approximation sub band and 6 high frequency sub bands for each of them. Denoising was done by applying the Donoho-Johnstone’s formula of universal threshold

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where is the threshold and M and N are the

dimension of the image and

Median(HF)/0.6745 where HF is the high frequency components of the image.

The fusion at the coefficient level is aimed at enhancing the signal content. Since the low frequencies represent the profiles of the image, the approximation coefficients are fused by weighted averaging rule and the weights are determined based on the entropy of the coefficients, as

LLr,b = (w1*LLm,b+w2* LLl,b)/(w1+w2) (7)

Where LLr,b is the resultant coefficient, LLm,b is the mean ratio sub band and LLl,b, the approximation sub band of the log ratio image, w1 and w2 are the weights of LLm,b and LLl,b respectively.

The high frequencies are fused by applying minimum local area energy rule. ie. the energy over a window of size 3x3 is calculated and the coefficient with the minimum value obtained so is chosen. It can be expressed as

(8)

Where is the resultant high frequency

coefficient, is high frequency coefficient

(LH,HL,HH) obtained on mean ratio operation and is the high frequency coefficient of log ratio operation.

Algorithm 2: To generate the change map from two temporal images

Input: two source images taken at two time points t1 and t2

Output: binary change map

Generate mean ratio image using equation 1 Generate log ratio image using equation 2 Apply UDWT decomposition on both images upto desired levels

Fuse the low frequency coefficients using equation (8) Apply equation (9) to generate the high frequency fused coefficients

Employ genetic algorithm to segment the coefficients into two groups-changed and unchanged

Generate a binary map of the segmented coefficients. Since we need only the change map, that label the changed and unchanged pixels, we apply a segmentation algorithm on the fused coefficients directly. Since the segmentation is a minimum error problem, it is an optimization problem too. Therefore, a genetic algorithm is employed on these coefficients to segment them into two groups-changed and unchanged. The recommended population size is fixed number, 20, in our experiment as to provide enough diversity and competition among the individuals. Since each individual represents the cluster centre of the changed and unchanged pixels, they have a dimension of 2d, where d is the dimension of the dataset. The chromosome that representing the candidate solutions are chosen randomly from the generated wavelet coefficients, based on without replacement strategy. The fitness function chosen was

(9)

where K is the number of clusters, vj is the centre of jth cluster and s the Euclidian distance and n is the number of data points . In the present work, the task is to divide the pixels into two groups with minimum error, for that, the fitness function is evaluated for each individual and the individual with minimum error is marked as the fittest one.

In order to ensure that the best individuals should move to the next generation, elitism is used in this study. 20% of the worst individuals are replaced by the best ones. The genetic operation, cross over, is done at a single point with random selection. The two strings from the selected point are swapped to produce new offspring. The third genetic operator, mutation is employed on the individuals based on a probability selected randomly. If the probability>a fixed value, the value at the randomly chosen position is multiplied by a number to mutate it. The iterations are repeated until the convergence criteria is met. The stopping criteria can be set in two different ways depending on the problem at hand. It can be set to a maximum number of iterations or the difference in current best and previous best approaches to a small epsilon value.

IV. DATA SETS

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Since change detection needs two images at different time stamps, we have chosen the first being the image acquired on August 5, 1986 and the second is the one that has been acquired on August 5, 1992, by the Landsat 5 MSS scanner. A small portion of the image of size 200 x 200 was clipped for the present study. We have chosen the first band of the image for our study. There is an decrease in the volume of water in the second dated image, thereby the lake bottom is exposed, mapping of which, is our target goal.

Data set 2: This is the satellite image of Dubai city acquired over an interval of a decade by Landsat 5. The first image is of year 2000 and the second is of year 2010. Over a span of 10 years, there has been huge changes occurred due to large scale built ups and roads and a major development was done in the gulf waters. This image is in portable network graphics format and has 3 bands.

Accuracy Metrics

The metrics chosen to evaluate the accuracy of the clusters were the two poplar metrics, the Percent Correct Clustering (PCC) and Cohen’s Kappa statistic. While PCC is concentrating on the correctness of segmentation, Kappa statistic takes account of the random chance of agreement as well. Mathematically they are expressed as

i) Percent Correct Clustering (PCC) =

(TP+TN)/(TP+TN+FP+FN)

Where TP is true positive, TN is true negative, FP is false positive and FN is false negative of the segmented pixels.

(ii) The Cohen’s Kappa statistic is a measure of the observed accuracy against expected accuracy.

[image:5.612.50.276.255.358.2]

Kappa coefficient= (observed accuracy – expected accuracy)/(1-expected accuracy)

Fig 3. Results of Lake of Tahoe, Reno with (a) UDWT fusion with K-means (b) UDWT fusion with

GA

V. RESULTS AND DISCUSSION

The experiments were done with the following objectives (i) to improve the quality of the difference image and thereby increase the accuracy of the change map. (ii) To evaluate the performance of the genetic algorithm in the segmentation process in generating the change map. Accordingly, we have used a fusion method in the UDWT domain to improve the quality of the difference image. GA was employed on the fused coefficients and the change maps were generated for the two data sets. The results of GA was compared against the results of K-means clustering, a well-established hard-clustering algorithm, at different levels. Visual analysis of the change maps obtained reveals the higher quality of GA.

Similarly, we have analyzed the quantitative accuracy of the image change map with the accuracy metrics as PCC and Kappa statistic and the results were compared with that of the two methods applied individually. From the Tables 1.1 and 1.2, it is evident that the PCC and Kappa statistics of the proposed method is higher than that of the other methods compared.

Fig 1. Multitemporal images of Lake of Tahoe, Reno (a) Image acquired on 5th_{Aug 1986 (b) image acquired on 5}th_{Aug 1992 c)}

Reference Map of Reno, Tahoe

Fig 2. Band 1 of Multi-temporal images of Dubai City (a) Image acquired in year 2000 (b) image acquired in year 2010 c)

[image:5.612.342.566.449.544.2]

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Fig 4. Results of Dubai city (a) UDWT fusion with

K-means (b) UDWT fusion with GA

[image:6.612.70.266.332.538.2]

From the Table 1.1, it is evident that the PCC and Kappa statistics of the proposed method is higher than that of the other methods compared.

Table 1.1

Results of various methods on Lake of Tahoe, Reno City

Method PCC Kappa

Log ratio 96.2650 0.511238888

Mean Ratio 95.8700 0.498491208 UDWT

fusion with GA (proposed)

96.3325 0.513715482

UDWT fusion

[image:6.612.74.266.499.626.2]

with Kmeans 96.3325 0.513715482

Table 1.2

Results of various methods on Dubai City

Method PCC Kappa

Log ratio 95.13875 0.493935043

Mean Ratio 94.540625 0.519336056 UDWT

fusion with GA (proposed)

96.6244 0.576102018

UDWT fusion

with Kmeans 95.1400 0.494002819

VI. CONCLUSION AND FUTURE WORK

In this paper we have discussed the methodology of a fusion method in the UDWT domain combined with the genetic algorithm, for the change detection using bi-temporal satellite images.

It detects the geographical changes occurred over an interval of time at two scenario- one on the natural changes in the Lake of Tahoe, Reno city and the other, to detect the changes occurred by built ups and construction inside the gulf waters of Dubai City, UAE. From the results, it is evident that the proposed technique is superior in obtaining change map compared to other few methods. GA, a soft computing population based algorithm has been used for the segmentation of the changed and unchanged pixels and found to be performing superior to other methods. A much better segmentation algorithm can delineate the pixels more realistically. Therefore, in the next work, we will be concentrating on a better segmentation algorithm in the soft computing paradigm.

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