Dual-Encoded Features from Both Spatial and Curvelet Domains for Image Smoke Recognition

Abstract

Visual smoke recognition is a challenging task due to large variations in shape, texture and color of smoke. To improve performance, we propose a novel smoke recognition method by combining dual-encoded features that are extracted from both spatial and Curvelet domains. A Curvelet transform is used to filter an image to generate fifty sub-images of Curvelet coefficients. Then we extract Local Binary Pattern (LBP) maps from these coefficient maps and aggregate histograms of these LBP maps to produce a histogram map. Afterwards, we encode the histogram map again to generate Dual-encoded Local Binary Patterns (Dual-LBP). Histograms of Dual-LBPs from Curvelet domain and Completed Local Binary Patterns (CLBP) from spatial domain are concatenated to form the feature for smoke recognition. Finally, we adopt Gaussian Kernel Optimization (GKO) algorithm to search the optimal kernel parameters of Support Vector Machine (SVM) for further improvement of classification accuracy. Experimental results demonstrate that our method can extract effective and reasonable features of smoke images, and achieve good classification accuracy.

1. Introduction

Generally, fire causes significant economic losses and probably lead to severe death. In order to avoid fire occurrence, many traditional fire detection technologies have been widely used. These methods are usually based on temperature sensors, humidity sensors, and traditionalultraviolet and infrared fire detectors. Since traditional methods need to sample combustion products for analysis, they are required to be placed in the vicinity of fire. In addition, traditional detectors are susceptible to external environment influences, such as airflow, dust. Traditional methods cannot provide us with detailed information about burning situation. Therefore, traditional smoke detectors are unreliable in open, large and special spaces.

In most cases, fire will be initially accompanied by the emergence of smoke, and smoke of ten lasts for a few minutes before flames emerge. According to this observation, visualsmoke detection methods detect smoke from videos or images, and they are able to give early alarms of fire.

Early smoke has special visual features, such as color, texture, and shape, which play an important role in fire detection. There are many texture feature extraction methods that have been proposed. Gray-level co-occurrence matrices [1] is a way to describe texture by exploring spatial correlation between gray values of neighboring pixels. LBP [2] provides abinary-coding feature extraction manner by encoding the relationship between central pixels and their neighboring pixels. HOG [3] extracts features of edges and gradients.

Many methods can achieve excellent performance by capturing multi-scale and multi-direction information in transform or frequency domains. Compared with othertransforms, Curvelet transform is strongly anisotropic and its needle-shaped elements providea high directional sensitivity to represent curved singularities in images. In contrast, wavelettransform shows a good representation only at point singularities because it has a poordirectional sensitivity. Additional directional-based transforms, such as Dual-Tree Complex Wavelet Transform (DTCWT) and Gabor Wavelets, provide more multi-direction information than Wavelets, but they still have limited directional selectivity. Ridgelet is suitable forrepresenting line singularities in objects, so it’s rarely found in practical applications [4].

To extract discriminative features, we propose a novel feature extraction based on spatial and Curvelet domains. The main contributions of this paper are listed as follows:

1) We use Curvelet transform to extract discriminative features from original images, and then encode these images consisting of discriminative Curvelet coefficients to generate LBP codes based on Curvelet domains.

2) We first aggregate histograms of LBP maps from Curvelet domains to produce a histogram image of size 256×50, and then encode the histogram image again to generate novel codes, which are called Dual-encoded Local Binary Patterns (Dual-LBP).

3) We concatenate histograms of Dual-LBPs from Curvelet domain and Completed Local Binary Patterns (CLBP) from spatial domain to generate dual-encoded features for smoke classification. Finally, we adopt Gaussian Kernel Optimization (GKO) algorithm to search the optimal kernel parameters of Support Vector Machine (SVM) for further improvement of classification accuracy.

2. Related Work

There are many methods proposed for smoke detection. Chenebert et al. [5] presented a flamepixel detection method in video images or still images using a non-temporal texture drivenapproach. The method did not use any time information. Chen et al. [6] used a color model based on RGB for fire smoke detection. However, there are many objects having the samecolor distribution as fire, so the method gives a false alarm inevitably for these fire-like object. Celik et al. [7] proposed a universal color model for fire pixel detection, and the algorith mused the YCbCr color space to separate chrominance and luminance components moreeffectively than other color spaces (such as RGB). Yuan et al. [8] proposed an accumulativemotion model based on integral image techniques. The model estimated movement directions of objects in real-time for analysis of smoke. Zhang et al. [9] proposed a real-time forest firedetection algorithm using artificial neural networks based on dynamic characteristics of fireregions segmented from video images. Yu et al. [10]presented a method by using color and motion features for video smoke detection. The method could distinguish smoke from objects with similar color distribution by involving motion features and color information, which greatly improved the reliability of video smoke detection. Toreyin et al. [11] achieved smokedetection based on edge magnitude differences, in which the characteristics of smoke such asmovement, flashing, edge blur and color were used. Once the scene lacks obvious edges orcluttered objects, the method raises false alarms.

Texture feature features play a key role in smoke detection, Ojala et al. [2] firstly proposed Local Binary Pattern (LBP) for texture classification. It is an efficient and simple gray-scaletexture descriptor, which captures spatial characteristics of texture. LBP features have demonstrated very powerful discriminative capability, low computational complexity, and low sensitivity to illumination variations.

To further improve the discriminative capability of LBP, many variants of LBP were proposed in the past decade. Yuan et al. [12] proposed an effective smoke detection method, in which features were extracted by concatenating histograms of local binary patterns (LBP) and local binary pattern variances (LBPV) from image pyramids, and an BP neural network was used for classification. Yuan et al. [13] presented sub-oriented histograms of LBP for images moke classification. Gubbi et al. [14] proposed a video smoke detection algorithm based on wavelet and Support Vector Machines (SVM) classification. Liao et al. [15] proposed Dominant Local Binary Patterns (DLBP) for texture classification by regarding the morefrequently occurred patterns as dominant features. Guo et al. [16] proposed a Completed LBP(CLBP) approach, which encoded the magnitudes and signs of differences between a centerpixel and its neighbors. CLBP provides excellent classification performance.

Above-mentioned methods extract features in spatial domains. Many methods achieverobust features from transform or frequency domains. Elaiwat et al. [17] proposed a multimodel Curvelet-based method for textured 3D face recognition. Each keypoint was detected across number of frequency bands and angles on 3D faces. Ucar et al. [18] presented an algorithm that was for facial expression recognition by integrating Curvelet transform and online sequential extreme learning machine (OSELM) with radial basis function (RBF) hiddennode having optimal network architecture.

Although Curvelet transform provides a powerful multi-scale capability to extract discriminative smoke features, Curvelet-based image classification methods are limited t of eatures, since the Curvelet coefficients are regarded as a holistic features extracted from the whole images [19]. To this end, we propose a duplex feature coding approach based on Curvelet transform to extract features from interpolated smoke images.

Many papers have been proposed to optimize kernel functions. Chapelle et al. [20] devised a gradient-based algorithm, which optimized a kernel function with multiple unconstrained parameters for SVM. Ghiasi-Shirazi et al. [21] considered the problem of optimizing a kernelfunction over translation invariant kernels for the task of binary classification. Wu et al. [22]proposed a direct method to build sparse kernel learning algorithms by adding one moreconstraint to the original convex optimization problem for sparse large margin classifiers. Ye et al. [23] considered the problem of multiple kernel learning (MKL) for regularized kerneldiscriminant analysis (RKDA), in which the optimal kernel matrix was obtained as a linearcombination of pre-specified kernel matrices. All above methods formulated the kernellearning problem as an optimization problem based on a special task, such as SVM.

3. Our Algorithm

The framework of our method is shown in Fig. 1. Our method consists of four main steps: Curvelet transform of original images, extraction of Dual-encoded Local Binary Patterns (Dual-LBP) on Curvelet coefficient sub-images, concatenation of histograms of Dual-LBP and Completed Local Binary Patterns (CLBP), and Gaussian Kernel Optimization (GKO) of SVM classification.

 

Fig. 1. The proposed smoke recognition framework

3.1 Curvelet transform

Curvelet transform was first proposed and structured with the tight frame by Candes and Donoho in 1999 [24]. Motivated by the need of image analysis, the second generation Curvelettransform [25] was introduced in 2005. It is not only simpler, but also faster and less redundant. Curvelets exhibit highly anisotropy and commendable directionality, which are beneficial forimage edge representation. Smoke image edges are always curved, so Curvelet is almost the optimal representation of a singular smooth curve.

A pair of window functions, which are called “radial window” and “angular window”, are defined as W(r) and V(t). These windows meet the following admissibility conditions:

\(\sum_{j=-\infty}^{\infty} W^{2}\left(2^{j} r\right)=1, r \in\left(\frac{3}{4}, \frac{3}{2}\right)\)       (1)

\(\sum_{l=-\infty}^{\infty} V^{2}(t-l)=1, t \in\left(-\frac{1}{2}, \frac{1}{2}\right)\)       (2)

Then, the frequency window U_j is defined:

\(U_{j}(r, \theta)=2^{-3 j / 4} W\left(2^{-j} r\right) V\left(\frac{2^{[j 2]} \theta}{2 \pi}\right)\)       (3)

where \(\lfloor j / 2\rfloor\) represents the integer part of j/2. Hence, the support of U_j is a polar “wedge” thatis defined by the support of W and V. Varying scales j and directions U produce multi-scaleand multi-direction transform.

These digital transforms are linear. We take a Cartesian array \(f\left[t_{1}, t_{2}\right]\left(0 \leq t_{1}, t_{2}<n\right)\) as input and get an output of digital coefficients from the digital Curvelet transform. The digital Curvelet coefficients are defined:

 \(c^{D}\left(j, \theta_{l}, k\right)=\sum_{0 \leq t_{1}, t_{2}<n} f\left[t_{1}, t_{2}\right] \overline{\varphi_{j, \theta_{1}, k}^{D}\left[t_{1}, t_{2}\right]}\)       (4)

where each \(\varphi_{j, \theta_{l}, k}^{D}\) is a digital mother Curvelet (the superscript D represents “digital”), t₁ and t₂ are spatial variable, and j, θ_l and k are scale, orientation, and position index, respectively.

In the first step of our method, bilinear interpolation is needed to generate normalized images of size 128×128 from original images with different sizes. The scale number of subbands is set to log₂(min(w, h)−3), where w and h are width and height of input images, respectively. Hence, the scale is 4 for a 128×128 image. Digital Curvelet coefficients are real-valued. The multi-resolution Curvelet transform of different scales have different characteristics. Lower scales, denoted as coarser scales, contain low frequency information whereas higher scales, known as detailed and finer scales, consist of high frequency information.

 

Fig. 2. The four-scale Curvelet coefficients of a smoke image

To implement Curvelet transforms, we first perform a 2D FFT on the interpolated 128× 128image. Then the 2D Fourier frequency plane of the image is divided into many parabolic wedges. Finally, an inverse FFT of each wedge is applied to find the Curvelet coefficients ateach scale j (j=1,2,3,4) and angle θ_l, and the range of l varies at different scales. An example of Curvelet coefficients at each scale is shown in Fig. 2. A red rectangular box stands for the coefficient map at one scale on one direction. The coefficient at scale 1 is displayed in the center. The coefficients at scale 2 on 8 directions and those at scale 3 on 16 directions aredisplayed in two loops around scale 1. Each block is equivalent to the pseudo polar tiling of the frequency plane with trapezoids.

There are two different digital implementations of Fast Digital Curvelet Transform (FDCT), which are based on Unequally Spaced Fast Fourier Transform (USFFT) and Wrapping Transform, respectively. In this paper, we use wrapping based Curvelet for feature extraction. The procedure of Curvelet based on wrapping is as follow:

(1). Apply the 2D FFT and obtain Fourier samples

\(\hat{f}\left[n_{1}, n_{2}\right],-n / 2 \leq n_{1}, n_{2} \leq n / 2\) , where n₁ and n₂ are frequency-domain variable.

(2). For each scale j and angle θl, form the product

\(\tilde{U}_{j, \theta_{l}}\left[n_{1}, n_{2}\right] \hat{f}\left[n_{1}, n_{2}\right]\)

(3). Wrap this product around the origin and obtain

\(\tilde{f}_{j, l}\left[n_{1}, n_{2}\right]=W\left(\tilde{U}_{j, \theta_{l}} \hat{f}\right)\left[n_{1}, n_{2}\right]\), where  \(0 \leq n_{1}<L_{1, j}\) and \(0 \leq n_{2}<L_{2, j}\)  for \(\theta_{l} \in(-\pi / 4, \pi / 4)\)

(4). By applying the inverse 2D FFT to each \(\tilde{f}_{j, l}\) , discrete coefficients \(c^{D}(j, l, k)\)are obtained. According to the above process, as shown in Fig. 2, we obtain a set of coefficient maps with four scales and sixteen directions from a normalized smoke image. Thus, we obtain coefficient maps containing coarse-to-fine and multi-directional texture information. The first and fourthscales contain only one coefficient map, and the second and third scales contain sixteen and thirty-two coefficient maps, respectively. It is worth noting that coefficient maps are indifferent sizes.

Being different from other traditional multi-scale transforms like wavelet transform, the coefficient map generated by Curvelet contains directional information of smoke, elevates ability to represent smoke textures and singularities along smoke edges. To extract features from these coefficient maps, we propose Dual-encoded Local Binary Patterns (Dual-LBP) to get information on each coefficient map.

3.2 Dual-encoded Local Binary Patterns

LBP is a gray-scale texture descriptor and can achieve rotation invariance after being mapped to RI (Rotation Invariant) pattern [2]. LBP captures spatial structures of textures in an image by encoding differences between one central pixel and its local neighborhood. However, structural frequency information is not involved in LBP codes. To solve this problem, we use LBPs to extract frequency structures of images from Curvelet coefficient maps with differents cales, orientations and locations.

In the Curvelet coefficients, the first scale contains only one coefficient map c(1,1), thesecond one contains sixteen coefficient maps c(2,l) (l=1, 2,…, 16), and the third one containsthirty-two coefficient maps c(3,l) (l=1, 2,…, 32), and the fourth scale also contains only onecoefficient map c(4,1). We compute LBP maps from coefficient maps of all scales. These LBP maps on coefficient maps can capture variations of coefficients in a local region for all scales. To avoid interpolation of coefficients, we employ a 3×3 rectangular neighborhoods instead of circular neighborhoods to compute an LBP codes as follows:

\(\operatorname{map}_{m, n}(j, l)=\sum_{p=0}^{p-1} s\left(c_{m, n}^{p}(j, l)-c_{m, n}(j, l)\right) 2^{p}\)       (5)

where  \(c_{m, n}(j, l)\) denotes the value of a central point (m, n) in a coefficient map \(c(j, l), c_{m, n}^{p}(j, l)\) is the value of the p_th neighbor of the center point (m, n), P is the number of neighbors, s(x) is a binarization function that returns 0 for negative values and 1 otherwise, and \(m a p_{m, n}(j, l)\) is just an original LBP code at pixel (m, n) for the coefficient map c(j, l).

Since we have a set of coefficient maps c(j, l), we obtain 50 LBP maps map(j, l) from thesecoefficient maps. LBP codes of each coefficent contain contrast information in local regions. We compute the histogram of each coefficient LBP code map map(j, l), formulated as follows:

\(\mathbf{H}_{j, l}(b)=\frac{1}{M N} \sum_{m=0}^{M-1} \sum_{n=0}^{N-1} \delta\left(\operatorname{map}_{m, n}(j, l)-b\right)\)       (6)

where δ(x) is a function that returns 1 for x=0 and 0 otherwise.

We can obtain a lot of histograms \(\mathbf{H}_{j, l} \in \mathbf{R}^{256 \times 1}\) from a set of coefficient LBP maps map(j, l). In our implementation, the first scale has only one histogram H_1,1, the second one generates 16 histograms H₂,_l (l=1,…,16), the third one obtains 32 histograms H_3,l (l=1,…,32), and the fourthscale also has only one histogram H_4,1. Therefore, we have 50 histograms. To combineinformation from different scales and orientations, we aggregate all these histograms together to form an LBP histogram map of size 256×50, formulated as follows:

\(\mathbf{M}=\left[\mathbf{H}_{1,1}, \mathbf{H}_{2,1}, \ldots, \mathbf{H}_{2,16}, \mathbf{H}_{3,1}, \ldots, \mathbf{H}_{3,32}, \mathbf{H}_{4,1}\right]\)       (7)

where H_j,l is just a column vector of the histogram map M, which represents the histogram of each LBP map c(j,l).

Hence, we obtain the new map M that is aggregated by normalized LBP histograms with 256 bins from fifty coefficient maps. Apparently, the size of the aggregated histogram map M is equal to 256×50.

In the second step of encoding, we apply the LBP encoding method again on the histogrammap M to generate another LBP map, defined as follows:

\(\mathbf{E}_{m, n}=\sum_{p=0}^{p-1} s\left(\mathbf{M}_{m, n}^{p}-\mathbf{M}_{m, n}\right) 2^{p}\)       (8)

where E_m,n is an Dual-LBP code at a center point (m, n), M_m,n is the value of the aggregated histogram map at the center point, and , \(\mathbf{M}_{m, n}^{p}\) is the pth neighboring value of the center point.

 

Fig. 3. Dual-Encoded features from Curvelet coefficient maps

Thus, we obtain another new LBP map from the histogram map M. Then we compute the histogram of the histogram map M. Dual-LBP extracts more details about frequent features from smoke images. The framework of Dual-LBP Encoding method is shown in Fig. 3.

3.3 Completed Local Binary Patterns

The original LBP is a computationally simple and efficient operator, but it only computes differences between a center pixel value and its corresponding neighbors’ gray values. The original LBP operator discards the magnitudes of differences by encoding the signs of differences in a 3×3 rectangular neighborhood.

Guo et al. [16] proposed CLBP, an extension of the original LBP operator. The CLBPoperator contains three operators, which are denoted as CLBP_S, CLBP_C and CLBP_M, respectively. The CLBP_S operator is just the same as the original LBP operator, whichencodes the sign of local differences to reflect directions of local gradients. While CLBP_Minvolves the magnitudes to preserve variance information. CLBP_C encodes the differences between local center pixels and the global one to represent whole image gray levels. CLBP_Cand CLBP_M are defined as follows:

\(C L B P_{-} C_{P, R}=s\left(g_{c}-c_{1}\right)\)       (9)

\(C L B P_{-} M_{P, R}=\sum_{p=0}^{P-1} s\left(m_{p}-c_{2}\right) 2^{p}\)       (10)

where c₁ is the average gray level of the whole image, c₂ is the mean difference magnitude oflocal neighborhood, g_c is the gray level of the center point, and m_p is the magnitude of the pthlocal difference, s(x) is defined as a binarization function, which is the same as Eq. (5).

3.4 Final features

We use CLBP to obtain three kinds of codes, which are CLBP_S, CLBP_C and CLBP_M, for each pixel. We compute a joint 2D histogram of CLBP_M and CLBP_C, and then reshapethe 2D histogram to a 1D histogram. Finally, we concatenate the 1D histogram with the histogram of CLBP_S to obtain the histogram H_CLBP of CLBP. The histogram E_m,n of Dual-LBP method captures frequency features of images in Curvelet domains. The CLBP method is encoded textures of images in spatial domains. We think that visual characteristics of smoke can be better captured if we combine spatial and frequency information. Hence, the final histogram H is obtained by combining E_m,n and H_CLBP, formulated as follows:

\(\mathbf{H}=\left[\mathbf{E}_{m, n}, \mathbf{H}_{C L B P}\right]\)       (11)

After extracting features, we will consider the issue of features classification. We input the obtained histogram H into SVM for training and testing.

Since Curvelet coefficients contain components of different frequency, which correspond todifferent spatial distribution, they reflect spatial texture structure. Dual LBP models therelations between different coefficients to intrinsically captures co-occurrence texturestructure. In other words, the proposed Dual LBP describes smoke textures in a macroscopic view [26].

3.5 Classification using SVM with GKO

We used Support Vector Machines (SVM) [27] to solve the image smoke classification problem. SVM is widely used in different fields such as clustering, classification, and dimensionality reduction. SVM is divided into two forms, which are linearly separable and linearly inseparable, respectively. Here we involve kernel trick to deal with linear inseparablefeatures. Kernel trick is thus a way to implicitly transform linear inseparable features of data onto a new space where the data becomes linearly separable [28]. The implicit new space is always higher-dimensional (possibly infinite) [29]. In general, the Gaussian kernel function, also known as Radial Basis Function (RBF) [30], to describe the relationship between every two feature vectors, as shown in Eq. (12),

\(\mathbf{K}\left(x_{i}, x_{j}\right)=\exp \left(-\frac{\left\|x_{i}-x_{j}\right\|^{2}}{2 \sigma^{2}}\right)\)       (12)

where\(\mathbf{K}\left(\boldsymbol{x}_{i}, \boldsymbol{x}_{j}\right)\) is the correlation or similarity between each two features x_i and x_j that are histograms H.

The earliest method of optimizing β=2σ² is to use cross-validation or grid search. One of the most well known methods is leave-one-out, which leaves only one sample as the test set and the remaining samples as the training set. Because each sample is repeatedly used duringiterations, the method consumes a large amount of computation time. Hence, we use Gaussian Kernel Optimization (GKO) [31] to optimize β in our experiments.

GKO is a kernel optimizing method for unsupervised learning, which is different from optimized methods of other supervised learning. The GKO method does not need any constraints, and the β value obtained by the GKO method can be used as a starting point for further optimization. Hence, we use the GKO method to calculate the optimal value of β in eq. (12). We define random variable \(Y_{i j}=X_{i j}^{2} / \sigma^{2}\) that satisfies the non-central Chi-squaredistribution with a degree of freedom one, where \(X_{i j}=\left\|x_{i}-x_{j}\right\|\) and the variance \(\sigma^{2}=\frac{1}{n^{2}} \sum_{i=0}^{n-1} \sum_{j=1}^{n-1}\left(X_{i j}-\mu\right)\). The optimal value of β can be obtained by the following equation:

\(\beta \approx\left\{\begin{array}{ll} {\sigma^{2} / 2.6} & {\lambda \leq 0.01} \\ {\sigma^{2} / L(\lambda)} & {0.01<\lambda<100} \\ {\lambda \sigma^{2}=\mu^{2}} & {\lambda \geq 100} \end{array}\right.\)       (13)

where L(λ) represents a function of λ. The relationship between λ and L(λ) is shown in Fig. 4, where λ=(µ/σ)², and \(\mu=\frac{1}{n^{2}} \sum_{i=1}^{n-1} \sum_{j=1}^{n-1} X_{i j}\)  represents the mean of the data set. The detailed proof of Eq. (13) is provided in [31].

 

Fig. 4. Relationship between λ and L(λ) when λ ∈(0.01, 100)

According to the above method, β is optimized. In our smoke recognition experiments, gamma =1/β = 4.6283 in the kernel function and the cost c=35 in the loss function.

4. Experimental Results and Analysis

4.1 Data sets

Several experiments were conducted on four data sets, each of which has an imbalanced number of smoke and non-smoke images. All images were manually cropped, resized and labeled as smoke images or non-smoke images. Smoke images of the data sets are easily distinguished by human eyes. The data sets are available at http://staff. ustc.edu.cn/~yfn/index.html. Smoke images of all datasets were resized to the size of 48×48 and converted to grayscale images for feature extraction. Table 1 lists the details of the data sets. We used Set1 for training, and Set2, Set3, and Set4 for testing. Some samples areshown in Fig. 5. It can be seen that both intra-class and inter-class variances of smoke and non-smoke images are very large.

Table 1. The image datasets

 

 

Fig. 5. Samples from the four data sets. (a) Smoke and (b) non-smoke images from Set 1. (c) Smoke and (d) non-smoke images from Set 2. (e) Smoke and (f) non-smoke images from Set 3. (g) Smoke and (h) non-smoke images from Set 4.

4.2 Implementation of compared methods

In order to verify the effectiveness of our method, we compared our method with somestate-of-the-art algorithms by the three evaluation criteria in [32], which are Detection Rate (DR), False Alarm Rate (FAR) and Error Rate (ERR). They are defined as follows:

\(\begin{aligned} &D R=P_{p} / Q_{p} \times 100 \%\\ &F A R=N_{p} / Q_{n} \times 100 \%\\ &E R R=\left(Q_{p}-P_{p}+N_{p}\right) /\left(Q_{p}+Q_{n}\right) \times 100 \% \end{aligned}\)       (14)

where P_p and N_p respectively denote the numbers of accurately detected true positive samples and negative samples mistakenly classified as positive samples, and Q_p and Q_n are the numbers of positive and negative samples, respectively.

4.3 Analysis of results

In our experiments, we used several feature extraction methods to validate the ability of ourmethod to distinguish between smoke and non-smoke images on the three test sets. Thesecompared methods are DRLBP [33], CLBP [16], LDBP [34], PLBP [35], PRICoLBP [36 ], MDLBP [37] LTrP [38] and DFD [39]. The compared LBP variants are all un-mapped for faircomparisons. The threshold for LTrP is set to 0.1 to demonstrate better performance, and g for RBF in SVM is set to 1/1383 for all other comparison features. For DFD, default setting is adopted to extract features.

We involve LBP and CLBP in our feature extraction step. Dual-LBP features based on the Curvelet domain and CLBP features on spatial domain are combined to form the final feature. In our CLBP, histograms of sign component and joint histograms of magnitude and centerpixel maps are cocatenated to form CLBP_S_M/C. Finally, we aggregate dual LBP and CLBP features (denoted as Dual-LBP + CLBP) as our final feature vector, whose dimension is 256+768=1024.

Table 2. Experimental results for smoke detection

 

From Table 2, we find that our method achieves lower FARs than other methods on threetesting data sets. MDLBP involves information across RGB channels, so it obtains the best DRs among all the methods. While all the other LBP variants are conducted on grayscale images. So it does not provide fair comparisons.

At the same time, the DRs got by our method are not obviously higher than other methods. Hence, ROC (Receiver Operating Characteristic Curve) is adopted to present a morecomprehensive comparison, as shown in Fig. 6. By varying classification threshold t from -1 to 1 at step 0.1, DR and FAR pairs are obtained at every step to plot ROC.

 

Fig. 6. ROCs of comparison methods on Set2, Set3 and Set4.

Although the DRs of our method do not exceed the ones of other methods obviously, the ROCs illustrate that our method outperforms others, which means that the best classification planes are not always at t=0.

The encoding step in our method can be replaced by any LBP-based methods. For instance, in Table 2 and Fig. 6, Dual-LBP + CLBP is adopted. Similarly, the other three combinations are Dual-LBP + LBP, Dual-CLBP + CLBP, Dual-CLBP + LBP. The experimental results of the 4 combinations are shown in Table. 3.

Although the FAR of our method is not the lowest on Set3 and Set4, the DR of our methodis highest and ERR is lowest. Overall, our Dual-LBP +CLBP performs best among all the combinations.

Table 3. Comparisons of 4 combinations for our method

 

It is notable that Dual-CLBP + CLBP performs worse than others on Set3 and Set4. Thereasons may be: 1) After Curvelet transform, an original image is decomposed into sub-bands. Low-frequency ones correspond to flat regions, in which the sign of gradient can bettercapture the invariance than magnitudes do. 2) There are correlations between Curveletcoefficients. Hence, the M and C components in CLBPs bring redundancy rather thanimprovement.

Lower FAR means lower accidental false alarm, which is of great significance for smoke classification, and it can reduce the serious consequences of false alarms. Therefore, ourmethod is of great practical application value.

Table 4. Performance comparisons on GKO and other versions of SVM

 

As shown in Table 4, we employ different parameter optimization methods to demonstrate the performance of GKO. We also compare our approach with the grid search, which is proposed in [30]. According to the experimental results, grid search method is proved not suitable for parameters optimization for different datasets. The GKO algorithm improves the accuracy of SVM.

Although the GKO step is time-consuming, it provides better classification performance and shorten the classifying time. Meanwhile, grid search consumes 214.1 seconds. Hence the GKO algorithm yields better performance than the grid search one. The computation time and the number of support vectors by the GKO algorithm are less than that of grid search on Set2.

5. Conclusion

In order to improve the performance of the smoke classification, we present a novel feature extraction method termed Dual-LBP, and we combine the proposed Dual-LBP and CLBP to improve the discriminative ability of features. The Dual-LBP method first adopts Curvelettransform to decompose smoke textures into coarse-to-fine components. Then LBPhistograms are extracted from the decomposed components, i.e., Curvelet coefficients, togenerate a histogram map to describe local distributions of coarse-to-fine smoke textures. Third, LBP encoding is applied to the histogram map to capture texture distribution relations between different frequencies.

The advanced feature encoding is explored, which connected Curvelet domains and spatial domains. Furthermore, our method discovers the potential relationship between each scale of the Curvelet coefficients and improves the smoke classification performances. Extensive experiments show that our method achieves improvements in smoke recognition over somestate-of-the-art methods.