Using Sharpness Image with Haar Function for Urban Atmospheric Visibility Measurement

Air quality affects human health, traffic safety and human life quality. The status of air quality can be indicated by the urban atmospheric visibility. The atmospheric visibility is traditionally the human-eye observed maximum distance at which outline of the selected target can be recognized. To replace the traditional measurement for the atmospheric visibility, digital image analysis techniques provide good visibility data which is established by the numerical index. These techniques provide good performance which is defined by the correlation between the observed visual range and the obtained index. In this paper, two high pass filters for atmospheric visibility monitoring are reviewed. Since the performance is affected by non-uniform illumination, such as shadow, a scheme which is called the sharpness image with Haar function is also introduced. Synthetic images, real images and actual atmospheric images are used to show the comparison of the performances. According to the results, the introduced method obtains higher relationship with human observed visibility than the other methods. We also show that obtaining the visibility indices with the proposed procedure can increase the similarity when the observed visibilities are the same.


INTRODUCTION
The influence of air quality not only affects human health, but also traffic safety and human life quality.Urban air quality is usually evaluated by the indicators such as atmospheric visibility.Low visibility strongly implies air pollution by ambient pollutants (Bishoi et al., 2009), particulate matter (Lin et al., 2008;Xu et al., 2008), or gaseous species (Sequeira and Lai, 1998).
The visibility is the traditional measurement which is defined as the maximum distance at which the selected target can be recognized (Horvath, 1981).In other words, the atmospheric visibility is a standard of human visual perception of the environment.Many researchers have applied some photograph processing methods for measuring visibility (Malm and Molenar, 1984;Larson et al., 1988) because the variation in human-eye observation could be high due to different personal characteristics (Malm, 1999).Moreover, several meters, such as the telephotometer (Agarwala et al., 2004), the nephelometer and the athelometer (Jayaraman et al., 2006), have also been developed to monitor visibility.
In recent years, the digital technologies are rapidly developing and applied to many applications.Digital image processing schemes have been widely used in industry, biology, pattern recognition, geographic information systems, environmental monitoring, machine vision and artificial intelligence (Luo et al., 2005;Chiu and Liaw, 2006;Gonzalez and Woods, 2008), etc.Digital camera can be used to measure the predetermined distance of a target for computation of visibility (Caimi et al., 2004).Expensive digital panorama camera is also used to determinate the visibility with Sobel operator (Baumer et al., 2008).Digital image data can be translated to specific brightness value, the difference between the building and its background (Luo et al., 2002).However, atmospheric visibility can be estimated by the digital image analysis techniques both in spatial domain and frequency domain.(Kim and Kim, 2005;Xie et al., 2008).
The concept of ideal high pass filter is proposed to measure urban atmospheric visibility (Luo et al., 2005).The Fourier transform and the Sobel operation are used to extract high frequency data in frequency domain and spatial domain, respectively.The ideal high pass filtered data is used to establish the visibility index.They also defined the performance by the correlation between the observed visual range and the obtained index.The correlation is the coefficient of determination, R 2 , which includes linear regression.If R 2 is close to 1, it means that the correlation is high.With the ideal filter, the R 2 result is less than 0.8.However, ideal high pass filters do not easily reveal the fine structures of a non-uniform illumination area, such as the shadow, of the urban image.
Illumination and reflectance components are characteristics of the digital image.The illumination is the amount of viewed source illumination incident on the scene.The reflectance is the amount of illumination reflected by objects in the scene.Slow and fast spatial variations characterize illumination and reflectance, respectively.The homomorphic filter operates these components separately with two or more parameters.The homomorphic filter can be used to improve the ideal filter (Pratt, 2007;Gonzalez and Woods, 2008).The homomorphic filter is also used to measure the visibility.The value of R 2 of measuring the visibility index via the homomorphic filter technology is close to 0.9 (Kutner et al., 2004;Sun et al., 2007).According to the correlation with the observed visual range, we can see that the homomorphic filter is better than the ideal high pass filter.However, using the homomorphic filter is complex because it is necessary to decide the parameters.
To improve non-uniform illumination sharpness, an algorithm with the Haar function is proposed (Yang, 2005).Compared to the homomorphic filtering technology, this method reveals the fine structures of the non-uniform image.Since objects in the urban atmospheric image may be shaded and outlines in the dim area are not illuminated enough to be recognized, the sharpness with Haar function is suitable for measuring urban atmospheric visibility.
This paper reviews a series of digital image analysis techniques with the ideal high pass filter (Luo et al., 2005) and homomorphic filter (Sun et al., 2008).The current work applies the sharpness with Haar function (Yang, 2005) to estimate the visibility index.The similarity is also used to compare the performance when the observed visibilities are the same.The experiments with synthetic and real images are used to compare the proposed procedure with previous schemes.

FOURIER TRANSFORM AND IDEAL HIGH-PASS FILTER
Since impaired visibility can not be detailed, the highfrequency components in the scene decrease.The highfrequency information can be used to estimate the visibility.We can use the Fourier transform and the ideal high-pass filter to separate the high frequency components (Luo et al., 2005).
The digital image can be described by a function, f(x, y), where the value of the function represents the brightness level at location of (x, y).The Fourier transform of the image with M × N size can be written as (Gonzalez and Woods, 2008) where (u, v) are the variables in the frequency domain.The ideal 2-D high-pass filter passes high frequencies and cuts off low frequencies at the cutoff distance, D 0 .The ideal high-pass filter function is defined as where D 0 is a positive integer and D (u, v) is the distance between (u, v) and the center of the frequency domain.
Finally, the filtered image can be obtained by the inverse Fourier transform.The visibility index is the average gray level of the filtered image.

HOMOMORPHIC FILTER
The ideal high pass filters do not easily reveal the fine structures of a non-uniform illumination area, such as the shadow, of the image.The homomorphic filter is useful for improving the non-uniform illumination area by brightness range compression and contrast enhancement.The homomorphic filter controls the filter function that affects low frequency and high frequency in different ways by choosing the parameters L and H.A homomorphic filter function can be defined as If we assume that L < 1 and H > 1, then the filter reduces the illumination (low frequencies) and increases the reflectance (high frequencies).In this paper, we set L = 0.5 and H = 1.1.After the homomorphic filter, the data is filtered again by a 2-D Gaussian high-pass filter which is defined as Similarly, the filtered image can be obtained by the inverse Fourier transform and the visibility index is the average gray level of the filtered image.

SHARPNESS WITH HAAR FUNCTION
The Haar function is an orthogonal base of the wavelet transform.In general, the orthogonal Haar function coefficient is typically 2 / 1 . In other words, when two data (p 1 and p 2 ) are inputted, they can be separated as 2 ) ( , respectively.In this section, we introduce how to obtain the sharpness image with Haar function (Yang, 2005).
We assume that the input image is described by a function, f(x, y), where the ranges of x and y are 0 ≤ x < M and 0 ≤ y < N, respectively.We compute the image in x direction and y direction.In the x direction, firstly, we set p 1 = f(2m, y) and ( 5) to be the two input points of the Haar function (where 0 ≤ m ≤ M/2).We also extract one pixel shifted, p 1 = f(2m + 1, y) and ( 7) to operate the transformation.Similarly, the y direction proceeds two times with one pixel shifted.Two input couples of the y direction are ) p 2 = f(x, 2n + 1) and ( 10) respectively (where 0 ≤ n ≤ N/2).We can see that the original image is separated into four subsets.In the separated subset, we set the original data (p 1 and p 2 ) into the sharpened data (p 1 ' and p 2 ') by the sign of the value of 2 ) ( . If the value is positive, we set p 1 ' = 14log(p 1 -p 2 + 1) and ( 13) otherwise, we set p 1 ' = 0 and (15) p 2 ' = 14log(p 2 -p 1 + 1).( 16) Finally, the sharpened image can be obtained by the sum of the results of four sub-images.
To estimate the visibility index, we combine the sharpened image with the homomorphic filtered image (without Gaussian high-pass filter).The combination is (the sharpened image) + c × (the homomorphic filtered image), where c is a combination weight.The same image database with Luo et al. (2005) is used to find the optimum value of c.The actual urban images are shot from the top of the Linden Hotel (a 42floor building in Kaohsiung, Taiwan) to the direction of Kaohsiung City Central Area (the north east direction).At the time of shooting the image, a trained investigator also recorded observed visibility.The image database took a total 172 images (database A) with observed visibility in four months.We compute indices of all 172 images with variant c.The relation between R 2 and c is shown in Fig. 1.We can see that the best value of c is 0.78 (because it makes the highest value of R 2 ).It is the same with Yang (2005) suggested.

EXPERIMENTS AND RESULTS
This paper compares with the performances of the Fourier transform (with the ideal high pass filter), the homomorphic filter and the sharpness with Haar function.The experiments include synthetic images and actual atmospheric images.The following describes the summaries of the experiments and results.
The first experiment uses the synthetic images.Fig. 2(a) shows an artificial building image, Fig. 2(b) shows the same artificial building with the shadow, Fig. 2(c) is a real image of a building and Fig. 2(d) is the same real building with the shadow.The real building images are taken by the same digital camera (Nikon S1) with the same setups which are 50 sensitivity (ASA scale), 1/200 seconds exposure and F 4.4 aperture.Since the shadow should not influence visibility index, with the same method, the indices of the same target should be the same.To show performance comparisons, this paper defines the similarity with two indices, v 1 and v 2 , % 100 2 We compute the visibility indices by above methods and the results (includes similarities) are shown in Table 1.
Results of the above experiments show that, the scheme of sharpness with Haar function makes the highest similarity.Since the sharpness with Haar function reduces the influence of non-uniform illumination, obtaining the visibility index by the sharpness with Haar function reduces the influence of the shadow.This study also uses two databases of actual urban images (they are the same as in Luo et al. (2005)) to show the performance.The database A includes 172 images which are shot from the top of the Linden Hotel to the north east direction in Kaohsiung, Taiwan (see SHARPNESS WITH HAAR FUNCTION section).The database B includes 226 images which are shot from top of the Linden Hotel to the south direction.Two example images of the database A and B are shown in Fig. 3.The image of the database A includes many big buildings.By contrast, the buildings in the image of the database B are small and occupies less one third of the image area.
From the database A, we try to compare the similarities of the three methods with shaded buildings compared to no shaded buildings in the same observed visibility.Fig. 4(a) shows an urban image obtained with less shadow.Fig. 4(b) shows another image and we can see that Fig. 4(b) shows more shaded buildings than Fig. 4(a).The observed visibilities of Fig. 4    the relationship is high.Fig. 5 and Fig. 6 show the relationships (by three methods) with database A and B, respectively.The line equations of the linear regression and R 2 are also shown on the figure.In the results of database A, we can find that the performances of the Fourier transform (with ideal high pass filter), the homomorphic filter and the sharpness with Haar function are R 2 = 0.77, R 2 = 0.86, and R 2 = 0.91, respectively.Similarly, in the results of database B, we can find that the performances of the Fourier transform (with ideal high pass filter), the homomorphic filter and the sharpness with Haar function are R 2 = 0.70, R 2 = 0.81, and R 2 = 0.87, respectively.According to the experiment results, the proposed procedure, the sharpness with Haar function, obtains the higher relationship with human observed visibility than the other methods.Moreover, since the performance of the database A (the images with many big buildings) is higher than the database B, the sharpness with Haar function is more suitable for the case of the urban atmospheric visibility measurement which the image includes many big buildings.

CONCLUSIONS
This paper introduces a series of digital image analysis schemes, based on high pass filters, for urban atmospheric visibility monitoring.Since the urban atmospheric images may be shaded and outlines in the dim area are not illuminated enough to be recognized, this paper introduces a procedure which is based on a sharpness of the nonillumination image.The experiments in this study use synthetic images, real images and actual atmospheric images to show the comparison of the performances between the Fourier transform, the homomorphic filter and the introduced procedure, the sharpness with Haar function.The performance is defined by the correlation, R 2 , between the observed visual range and the obtained index.Results show that the sharpness with Haar function obtains higher relationship with human observed visibility than the other methods.We also show that obtaining the visibility indices with the proposed procedure can increase the similarity when the observed visibilities are the same.The sharpness with Haar function is more suitable for the case of the urban atmospheric visibility measurement.

ACKNOWLEDGEMENT
The authors would like to thank Dr. Chung-Shin Yuan and Dr. Chin-Hsiang Luo for providing the experiment samples (database A and B).This study is supported partially by the National Science Council of Republic of China, Taiwan, NSC 97-2221-E-324-041.

Fig. 1 .
Fig. 1.The results of finding the optimum c value (the combination weight).

Fig. 2 .
Fig. 2. The synthetic images.(a) The artificial building without shadow, (b) the artificial building with shadow, (c) the real building without shadow and (d) the real building with shadow.
Fig. 3.The example images.(a) an image of database A and (b) an image of database B.

Fig. 4 .
Fig. 4. The actual urban images (with different observed visibilities) which are shot on cloudy day and sunny day.(a) 3 km without shadow, (b) 3 km with shadow, (c) 5 km without shadow, (d) 5 km with shadow, (e) 12 km without shadow, and (f) 12 km with shadow.

Fig. 5 .
Fig. 5.The result of actual urban images with database A.

Fig. 6 .
Fig. 6.The result of actual urban images with database B.

Table 1 .
The obtained indices and similarities of the synthetic images.

Table 2 .
The obtained indices and similarities of the actual urban images.