* Corresponding authors: Department of Computer Science & Engineering, Rajshahi University of Engineering & Technology, Rajshahi-6204, Bangladesh E-mail addresses: [email protected] (Md. Ali Hossain)
1 Journal of Engineering and Applied Science Vol. 03, No. 01, pp. 01–11, June 2019
Optimized Subspace Selection based on Dominant Band Detection from Hyperspectral Images
Md. Ali Hossain*, Subir Sarker, Md. Rabiul Islam
Department of Computer Science & Engineering, Rajshahi University of Engineering & Technology, Rajshahi-6204, Bangladesh
ARTICLE INFORMATION ABSTRACT
Received date: 30 Jan 2019 Revised date: 24 April 2019 Accepted date: 01 May 2019
An effective subspace of the hyperspectral data cube is used to provide accurate spectral variations of different ground objects and it can be achieved through feature extraction/selection or a combination of both.
However, detection of an informative subspace is a challenging task and most of the existing approaches depend on the global measure and supplied training samples which may not be available always. For instance, Principal Component Analysis (PCA) extracts the features based on the global variance and showed poor performance when the samples are not linearly correlated. In this article, a novel approach for unsupervised subspace detection has been proposed, in which, the quality of the selected images is determined based on the amount of local structure of the image contents. The strengthen part of this approach is its effectiveness while the training samples are not available for modelling the classifier and it is named as Dominant Bands Detection (DBD) technique. It combines both the spectral and spatial information of image bands in a feasible way to find out the most relevant subspace. The proposed method has been tested on two real hyperspectral images and obtain (98.41%) of accuracy which outperforms the baseline approaches.
Keywords
Feature extraction Feature selection Dimensionality reduction Image classification Curse of dimensionality Hyperspectral images Remote sensing technology
1. Introduction
With the recent advances in remote sensing technology, hundreds of narrow contiguous spectral image bands can now be captured using a hyperspectral sensor in order to provide the accurate spectral information of the ground objects [1-3]. Although, the spectral reflectance of the hyperspectral image provide the finer details of the ground objects, these dataset presents many challenging while working on it [4-7]. A major challenge on the use of hyperspectral images lies in the development of suitable techniques for processing the large volumes of data. At present, the NASA Airborne Visible Infrared Imaging Spectrometer (AVIRIS) sensor contiguously captures 224 image bands in the wavelength range 0.4-2.4 μm with a spectral resolution of 0.01μm [1, 6, 8-12]. This means that, the captured data provides greater details of the spectral variations of ground objects for the task of classification. From Figure 1(a), it
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2 is seen that the spectral reflectance of the vegetation, hay-windrowed and woods have the sufficient variations to identify each from other.
However, these large volumes of image bands imply high dimensionality data in a machine learning framework.
Moreover, if the ratio of the number of training samples and input dimension becomes small, the classification accuracy of the test becomes smaller due to the poor generalization of the training results and this effect is known as the Hughes phenomenon or curse of dimensionality [10, 12, 13-15]. It can be seen from the Figure 2 that the accuracy starts to decrease as the image bands increases for classification. The highest accuracy reached when there are 17 image bands used for classification. Therefore, feature reduction is strongly encouraged to improve the ground object detection.
(a) (b)
Figure 2: Curse of dimensionality issues, classification accuracy starts to decrease after a certain time.
Redundancy of the information is another challenge of hyperspectral images, since the images are sensed in very close and contiguous spectral bands, some bands are highly correlated both spatially and spectrally [16, 17]. From Figure 1-b, it can be seen that there are large white blocks which belongs to correction value of close to 1. Therefore this redundant data can be removed without losing important information. It can also be observed that all the image bands are not equally important for a specific application. Therefore, the aforementioned challenges can be addressed through dimensionality reduction via feature selection/extraction or both [18-20]. In feature extraction, a new set of features are generated from the original features/image bands via linear or nonlinear transforms using supervised or unsupervised approaches.
0 50 100 150 200
20 30 40 50 60 70 80
Input spectral bands
Classification accuracy %
Figure 1: (a) The spectral reflectance of a vegetation, hay-windrowed and woods pixels, (b) Spectral correction among the image bands of Indian Pine hyperspectral image. Hence white belongs to 1 and black colour belong correlation value 0.
3 Linear Discriminant Analysis (LDA) [4] and Principal Component Analysis (PCA) [1, 2, 19] are well known supervised and unsupervised linear feature extraction methods, respectively. The LDA uses the first and second order statistics of the data to find the largest ratio of between class variance and within class variance in the new subspace.
A major limitation of the LDA approach is that it can only generate M−1new features, where M is the number of input classes of interest. Sometimes the M-1 classes may not be optimal for the task of classification. LDA has another limitation of handling only the normal like distributed data. Another major consequence of this approach is that, it cannot be applied if the ground truth reference image is absent. Although PCA removes the mandatory requirements of the reference images and represent the data optimally in terms of maximal global variance and minimal mean squared error between the new generated data and the original. The new features are also un-correlated. However, PCA does not emphasize the local structure of the image bands while generating the new dataset during eigen analysis, so there is no guarantee that the selected PCA features are the best for classification [1, 5, 7, 20, 21]. Since PCA considers only global variance, there may have some classes in the input images which are very small and hardly affect by the overall variance and hence are not represented in the selected principal component images.
Figure 3: A snapshot of dimensionality reduction approach.
Another popular supervised feature selection method is utilizes the Jeffries-Matusita (J-M) distance which measures the separation between a pair of classes after each of them is assumed to have a normal like distributions [8]. The limitations of this method, however, include a strong dependence on the normally distributed training data, ineffective class pair wise treatment data [8, 9, 22-24].
Alternatively, the proposed Dominant Band Detection (DBD) method excavates the inherent properties of the input hyperspectral image data. The proposed DBD method allows selecting dominant bands (e.g., which contains relevant information), and then turn the dominant bands detection problem into a scale selection problem based on the basic idea that the hyperspectral image is not only a detection problem but also a hyper scale representation of the objective world. The DBD method selects the important image bands which describes the image contents maximally using local extrema points. This measurement is termed as the scale space of an image band therefore selects the image bands having maximum scale space among the neighboring bands. The number of dominant bands depends on the input hyperspectral image itself. Therefore, the proposed method is able to provide the idea of where to stop the selection.
In Figures 3&4, a generic idea of feature selection followed by classification is presented. The later part of this paper will present the technical details including all explanation for the task image band selection. This article is organized as follows. Section II gives the definition of dominant bands and how the subspace detection problem becomes the scale selection problem, proposed DBD method in details. Section III discusses the experimental results and analysis of the DBD method. Conclusions are presented in section IV.
2. Dominant Bands and Scale Representation 2.1 Dominant Bands
The dominant bands are those image bands that hold the inherent properties of the ground objects captured and the proposed DBD should find out these image bands. Therefore, the selected image band is termed as dominant bands the proposed method is named as Dominant Band Detection. The next research question is: how to select these dominant bands, because, all the bands are not dominant. Since, different ground objects has different reflection characteristics to the solar spectral, and only some ranges of spectral is suitable to separate the two objects clearly.
According to the assumption, it can be summarized the basic properties of supreme bands. (i) These are the bands Input remote sensing image
FS
Detected subspace/subset of
images
Image Classification Object identification Preprocessing for classification
Follow-up-task
4 that can characterize as many objects as possible of the earth surface. (ii) These are the rare bands in the input 3D image data volume. (iii) These are only determined by the object in the input hyperspectral image. According to the definition of dominant bands it can be declared that dominant bands are informative image bands. Noisy band is not dominant band because it is unable to characterize the object.
2.2 Hyper-Scale Representation
The pixel level spectral reflection curves of vegetation, hay-windrowed and woods shown in Figure 1-a reveals that different intervals of the spectrum are determined by different mechanism in order to identify the objects. From Figure 1-b, it can be seen that the image band groups 40-53 can easily characterize the woods classes while comparing vegetation and Haywindrowed as this bands shows very strong reflectance than the others. This property is utilized in order to determine the extreme points in an image so that the contents of the image are formulated quantitatively.
Therefore hyperspectral image is considered as hyper spectral representation of the objective world [2]. According to these facts we believe that the hyperspectral image is also a hyper-scale representation of the objective world. Brady et al. noticed dominant band, scale detection and content description are intrinsically more related [8]. When it comes to hyperspectral image, it is most logical to that the dominant bands and scale detection are highly related. That is why; scale detection technique is able to characterize the object in hyperspectral image [7]. Thus the dominant band detection problem is turned into a scale detection problem.
2.3 Scale Detection and Dominant Band Detection
According to the definition of dominant band it is valuable and meaningful than other neighboring bands, the fact is without any evidence, and it really says nothing about it is quite difficult to tell which scale is more appropriate than other scale without any evidence. Fortunately there’s a method to select appropriate scales in image content detection technique. The main principle of this scale detection technique is that local extrema over scales of different combinations of normalized scale invariant derivatives are the likely candidates to correspond to interesting structures [2]. Moreover, the scale detection methodology is very powerful techniques in much research domains when it involves feature extraction and description. In following, the Dominant Band Detection method for selecting a subset of image bands from hyperspectral data cube has been explained in details.
2.4 Proposed Band Detection Method
In the proposed DBD method, band selection is performed based on the value of scale representation and this scale is highly related to image structures (e.g. features) such as blob, junction, edge, texture etc. [8]. The scale is calculated based on the structures of the image contents. In DBD method, the extrema points are used to determine the proper scale value or dominant image band. Since the local extrema points and its derivatives are appropriate in scale selection, we first determine the polynomials of the hyperspectral image derivatives. For a given hyperspectral image
‘HyperI’, the polynomials of the hyperspectral derivatives is given bellow:
𝐷𝑒𝑟𝑣 𝐇𝐲𝐩𝐞𝐫𝐈 = ∑ (𝑎𝑖) ∑𝐽𝑗=1(𝐇𝐲𝐩𝐞𝐫𝐈𝑝𝛽𝑖𝑗)
𝐼 𝑖=1
(1) Where multi index notation is, HyperIpβij=HyperIxmijnij denotes a derivation of order |βij|= mij+nij taken in the horizontal (X) and vertical (Y) direction. From linear algebra, we know that the trace and determinant of Hessian matrix has a good ability to describe the local structures of input image [14], therefore, we use the Hessian matrix to measure the quality of an image band. If the trace and determinant of hyperspectral image derivatives are defined as
“trace HyperI” and detHyperI, the can be defined as:
traceHyperI= HyperIxx+ HyperIyy (2) 𝐝𝐞𝐭 𝐇𝐲𝐩𝐞𝐫𝐈 = 𝐇𝐲𝐩𝐞𝐫𝐈𝐱𝐱𝐇𝐲𝐩𝐞𝐫𝐈𝐲𝐲 − 𝐇𝐲𝐩𝐞𝐫𝐈𝐱𝐲𝟐 (3) The etrema points are those points which shows strong variations spectrally and spatially therefore become local extrema with respect to the image structures. For instance a point x is said to be local extrema if its derivative is higher
5 than any of its neighborhood. Since the process of calculating the band responses on trace or determinant matrix are the same, so we will consider only the trace of the hyperspectral image in the successive explanation.
2.5 Measuring the Response of Each Image Band
A band is said to be dominant if it has a lot of extrema points therefore the band can characterize different ground objects Due to the affecting of local extrema by noise, we take the mean of local extrema. However these points may be affected by noise and a mean of local extrema is suitable in such case. Moreover, to reduce the sensitivity we squared it before further processing and the new trace becomes as follows:
traceSquareHyperI = (HyperIxx+ HyperIyy)2 (4)
After determine the traceHyperI, the value and location of the extrema in it is recorded to calculate the response of each image band. The response of image bands traceRespns is calculated by the sum of extrema values divided by the number of extrema points. This traceRespns denotes the ability of each image band to characterize the objects contained in it. Therefore the image bands are ordered based on the high value of the traceRespns. traceExtremum = imregionalmax (traceSquareHyperI) (5)
traceRespns = squeeze (sum ((sum (traceSquareHyperI.* traceExtremum, 1)), 2)); (6)
traceNumber = squeeze (sum ((sum ( traceExtremum, 1)), 2)); (7)
tracRespns = traceRespns ./ traceNumber (8) Finally the image bands are ordered based on the high value of tracRespns to determine the resultant subset of images.
According to the definition of these image bands are the dominant bands as they have high responses than the others.
Therefore these image bands are suitable for task of classification in order to identify the ground objects appropriately.
The entire process is shown in the following Figure 4 using a block diagram.
Figure 4: Proposed Dominant Band Detection Method.
Input Hyperspectral Image I
Calculate the Hessian Matrix H Apply Filter to remove noisy image
Calculate the determinantand trace of the Hessian Matrix H Calculate the bands response
Order the image bands based on the high value of band response
Apply the selected bands to classifier
6 3. Experimental Results and Analysis
To verify the performance of the proposed DBD method, two different real hyperspectral images have been tested, and the experimental results are compared with other baseline band detection methods. In the experiment Kernel Support Vector Machine (KSVM) classifier used to verify the classification performance of different band selection techniques. The performance of different band detection techniques are compared based on the classification accuracy.
Higher the classification accuracy means the selected bands are more suitable to identify the required ground objects.
3.1 Data Set Description
Indian Pine: The first hyperspectral image is the Indian Pine dataset which was acquired by the NASA AVIRIS sensor over the agricultural area of Northwestern Indiana in 1992. This dataset covers the mixed agricultural crops including Corn, Soybean, Wheat, Haywindrowed, Woods, roads and a small built-up area. Each image band of the 3D data cube contains 145 × 145 pixels, and the cube contains 224 spectral image bands in total. There are few image bands affected by sensor noise and water absorption whose index are 1-3, 103-112, 148-165 and 217-220 [6]. These noisy bands are filtered and removed at the pre-processing steps of experiment. There are 16 classes of interest in the input image and all the classes are considered for the evaluations. However few classes may avoid as they do not contain sufficient samples to describe the intrinsic properties of the input classes [15]. The description of the classes and the input dataset with its ground-truth reference images are presented in the following Table 1 and Figure 5.
(a) (b)
Figure 5: (a) Input Indian Pine hyperspectral image (Channels Red, Green, and Blue: 50, 27, 17) and (b) its Ground- truth reference image with 16 classes.
Pavia center: The second tested data set is Pavia center University data as shown in Figure 6. These scenes are acquired by the ROSIS sensor during a flight campaign over Pavia, northern Italy. The number of spectral bands is 103 for Pavia University. This image contains 610x610 pixels for each image band and therefore the dataset becomes 610x610x103. Similarly, some of the image bands contain no information and have to be avoided as well before the experimental analysis. The spatial resolution is 1.3m and contains 9 different classes as described in ground truth reference image [15].
3.2 State-of-the-Art-Methods
The performance of the proposed method is compared with following three other baseline approaches:
(i) Volume Gradient Based Band Selection (VGBS) [2]
(ii) An Enhanced Fast Density Pick Based Clustering (EFDPC) [11] and
(iii) Dual Clustering Based Hyperspectral Band Selection by Contextual Analysis (DCCA) [12].
7 Table 1: Input classes of interest and their respective samples number for the Indian Pines scene
For # Class Samples
1 Alfalfa 46
2 Corn-notill 1428
3 Corn-mintill 830
4 Corn 237
5 Grass-pasture 483
6 Grass-trees 730
7 Grass-pasture-mowed 28
8 Hay-windrowed 478
9 Oats 20
10 Soybean-notill 972
11 Soybean-mintill 2455
12 Soybean-clean 593
13 Wheat 205
14 Woods 1265
15 Buildings-Grass-Trees-Drives 386
16 Stone-Steel-Towers 93
Table 2: Input classes of interest and their samples number for the Pavia Center University scene
Class Samples
1 Water 824
2 Trees 820
3 Asphalt 816
4 Self-Blocking Bricks 808
5 Bitumen 808
6 Tiles 1260
7 Shadows 476
8 Meadows 824
9 Bare Soil 820
Figure 6: (a) Pavia Center University hyperspectral image and its (b) ground-truth reference image.
8 The VGBS method selects the bands with the maximum determinant of the covariance matrix with a fast computation strategy. The second method EFDPC is an enhanced clustering method; it redefines the ranking score by squaring the weight of distance term. The third method DCCA combines both the spatial-spectral information of the input data for the task of feature selection. These three methods are chosen from the current literature as they have higher classification accuracy than many other band detection methods such as ID, MVPCA, DBDCAN, AP, etc., [2-3, 11- 12].
3.3 Classification
The Kernel Support Vector Machine (KSVM) classifier is used to assess the performance of the proposed DBD technique and the baseline approaches. The hyeprparmeter of the KSVM classifier has been tuned to the appropriate values after rigorous learning using 10-fold cross validation technique. The one against all KSVM parameters are used as: ‘Standardize’, 1; ‘KernelFunction’, ‘rbf’; ‘BoxConstraint’, 10; ‘KernelScale’, ‘auto’; ‘Coding’, ‘onevsall’ for generating the training model.
3.4 Results and Discussion
Indian Pines: The classification results of the studied approaches on the Indian Pine hypespectral image are shown in Figure .3(a). From the analysis presented in Figure 7, it can be seen that the proposed DBD methods obtains the highest classification accuracy (79.54%) with only a 15 features. To achieve the similar accuracy, the other baseline approaches requires much more image bands than DBD and it is at least double in number in compare to DBD selected features. The DBD works well because the DBD measure the quality of the selected bands based on the amount of local structures contained in the images. Hence, it orders the quality of the features using a scale/band response depending on the structure of the image contents. A summary of the overall accuracy of the studied approaches has been presented in Table 4 for clear understanding of the improvement. The selected features are also listed in Table 3. This analysis on the Indian Pine hyperspectral images reveals the fact that the proposed DBD method outperforms the base line approaches studied.
Figure 7: overall classification accuracy versus the selected bands of different methods on Indian Pines hyperspectral image.
Table 3: The selected image bands using DBD on Indian Pines image.
Response Selected Bands
Dominat Bands of HyperI (15 bands)
B22 B42 B48 B54 B62 B72 B90 B123 B131 B136 B173 B183 B192 B198 B203
9 Table 4: Overall accuracy using DBD and others methods on Indian Pines image
Methods Overall Classification Accuracy (%)
DCCA 70.86
VGBS 73.93
EFDPC 72.71
DBD 79.54
Pavia Center: The performance of DBD method along with VGBS, EFDPC and DCCA on Pavia Center University are shown in Figure 8. The classification results clearly show the improvement achieved with proposed DBD method.
The order of the selected dominant bands and overall classification accuracies are presented in Tables 7 and 8.
Table 5: Selected Bands using DBD on Pavia Center University image.
Response Band select
Dominat Bands of HyperI (8 bands) B11 B18 B31 B37 B46 B54 B67 B78 Table 6: Overall accuracy using DBD, EFDPC, VGBS and DCCA on Pavia University Data.
Methods Overall Classification Accuracy (%)
DCCA 80.25
VGBS 74.93
EFDPC 75.71
DBD 98.41
Figure 8: Overall classification accuracy versus the selected bands of different methods studied on Pavia center University image.
3.5 Complexity Analysis
The proposed DBD technique is also suitable in terms of time complexity. For an M x N x R hyperspectral image the time complexity of the proposed and the existing approaches is listed in the above table.
Table 7 shows that, the computational complexity of DBD algorithm is O(MNR) which is linear where M, N and R stands for number of rows, columns and number of bands. The computational complexity of other start-of-the-art algorithms, such as VGBS [2], EFDPC in [11], are O(max (R4, MNR2)) and O(2MNR2), respectively.
10 Table 7: Computational Complexity of DBD
Steps Complexity
HyperIx,HyperIxy, HyperIxx, HyperIyy
3MNR
traceHyperI 2MNR
traceExtemum 3MNR
traceRespns 2MNR+R
traceNumber 2MNR+R
traceRespns R
traceIndexvalues 2R
4. Conclusion
It is believed that there must have some intrinsic properties in hyperspectral image, and there is a reasonable way to combine spatial-spectral information to obtain the underneath information. In this article this idea is utilized and a novel unsupervised band selection technique is developed. The proposed method is able to measure the amount of local structures in each of the image bands. The quality of the selected image bands is analyzed for classification. It is seen from the analysis on real hyperspectral images that the selected bands have the ability to address the curse of dimensionality issue as well as improve the over classification performance. The strength of the proposed method is its applicability when the ground-truth reference image or training samples are unknown. However there is still capacity to improve the method as local extrema points have the possibility of affecting by noise. This issue will be studied in the future work.
Acknowledgement
Authors want to express gratitude towards the respected Professor Dr. David A. Landgrebe, Purdue University, West Lafayette for providing the Indian Pine Hyperspectral image and its ground truth reference.
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