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1. AGH University of Science and Technology, Faculty of Mining Surveying and Environmental Engineering, Department of Geoinformation, Photogrammetry and Remote Sensing of Environment, Krakow 30-059, Poland
2. MGGP AERO Company, Tarnow 33-100, Poland
Received: July 4, 2011 / Accepted: August 5, 2011 / Published: February 20, 2012.
Abstract: The paper presents the method of the valuation of random noise in the photogrammetric images, based on wavelets. The proposed method involves the analysis of the dynamics of the components of wavelet decomposition on several resolution levels. The hypothesis was made that the noise-free images are characterized by systematically growing variances of the single components with growing decomposition. This hypothesis was studied on several dozen fragments of airborne images recorded both with a photogrammetric analogue camera and digital camera. For all the studied photos taken with a digital camera, the hypothesis of growing variances of details was confirmed. The images from an analogue camera had different dynamics of variance, and the cause was recognized as random noise, caused by the grains from of the photographs. Referring to earlier applications of wavelets to noise evaluation, the proposed method is characterized by smaller dependence upon the structure and texture of the image.
Key words: Noise, camera, wavelets transform, decomposition, variance.
1. Introduction
When at the ISPRS Congress in Amsterdam, in 2000, the companies of Leica and Z/I Imaging showed the prototypes of first photogrammetric digital cameras, few people believed that within one decade the analogue cameras would be changed into digital ones. In those times people thought that photogrammetric technology, based on analogue photographs taken by cameras that had been improved for years, then scanned and converted into a digital form, did not need new solutions. Yet the images from digital frame cameras had at first much smaller size than those that could be achieved by scanning analogue images. The problem of the smaller size of the image from a digital camera has not been solved yet, but now it is not as significant as it was in the first cameras. Let’s notice that an analogue image of 23 cm × 23 cm, scanned with the resolution 2000 dpi, has the size of about 325 Mega pixels, while the image from the newest digital camera DMC II by Z/I Imaging is of 250 Mega pixels. Thus, in terms of the size the images of the photogrammetric digital camera have not been made equal to the scanned analogue images, yet. So why analogue cameras of air borne photogrammetry are now used only sporadically and mainly digital cameras are used?
The answer to the above question is much better radiometric quality of images taken by digital cameras. A better radiometric quality not only does improve the quality of the ortho-photomap, making the most popular photogrammetric product, but—what is more important—allows higher level of the automatication of the technological process. The application of images from digital cameras accelerates the process of aero-triangulation and the creation of the digital terrain model (DTM).
One of the elements of radiometric quality, apart from radiometric resolution, contrast and tonal
matching, is the noise level in the image. Noise can be defined as a signal, which is unfavourable, appears accidentally or systematically and disturbs the image diminishing its information value [1]. In the case of scanned analogue images, the main source of random noise is coarse photographic emulsion and instability of the scanner’s detectors. The image taken by a digital camera can contain random noise arising during the formation of the image during the process of sampling, coding, compression and transmission of the image.
The article proves that images taken with an analogue camera and then scanned contained much higher level of noise than images taken with a digital camera. As a tool of studying noise in the images, wavelet transformation was applied.
2. The Application of Wavelet Transformation for the Detection of Noise in the Images
Wavelet transformation is replacing the classical record of the image as a spatial function of 2D space. It is a frequency-spatial representation of the image. The method of marking developments of wavelet images with the multi-stage decomposition, using one-dimension filters were applied separately for verses and columns of the image, given by Mallat [2]. In the wavelet development of image I four components occur: one so-called coarse (LL) and three detail, defined as vertical (LH), horizontal (HL) and diagonal (HH). The characteristic feature of wavelet transformation is the possibility of its continuation in the relation to the selected components, which usually better develops the coarse component (such a scheme was accepted in the study). Fig. 1 presents the classic scheme of image wavelet decomposition according to Mallat [2]. This scheme was used in these studies. Every subsequent image wavelet decomposition consists of four components half a size (in linear terms). For example if the size of the original image is 1024 × 1024 pixel, the size of all the four components on the first resolution level is 512 × 512, on the second 256 × 256, etc..
The application of wavelet image representation in the assessment of the image radiometric quality was first proposed by Simoncelli [3, 4], who noticed that the distribution of the wavelet coefficients of detail components shows sharp maximum in point zero and good symmetry, while the flattening of the histogram is correlated with the presence of noise in the image. However, this method is not objective, because the results are strongly influenced by the structure and texture of the image [5].
One of the properties of wavelet transformation is preserving the energy of the image during its decomposition [2]. In case of decomposition, on one resolution level it obtains:
E(I)?E(LL1)?E(LH1)?E(HL1)?E(HH1)(1) where:
E(I) = energy of image I;
E(LL1) = energy of coarse component LL on first level of decomposition;
E(LH1), E(HL1), E(HH1) = energy of detail components LH, HL, HH (on the first level of decomposition).
Further decomposition of coarse detail is written
From Eq. (5), it can be concluded that the sum of the variances of wavelet components normalized by the variance of the image equals 1. It is worth emphasising that one of the variables of Eq. (5) is the level of decomposition R, which means that the sum of the variances of wavelet components is the same for each wavelet development of the image. Fig. 2 shows graphic interpretation of Eq. (5), assuming two things:
? The number of decomposition levels R = 3;
? The curve combining two subsequent values of variance is growing.
The first assumption is arbitrary, a relatively small number of decomposition levels was selected, but was sufficient for detecting the trends in variance changes. The second assumption is a study hypothesis, which has to be explained. Wavelet transformation according to the Mallat scheme is a combination of low-pass and high-pass filtration, with simultaneous dyadic reduction of the image size (Fig. 1). The idea of every decomposition is localizing the selected edges (places where the brightness changes) of the image in fine components and leaving the remaining image information in the course component. On the first level in components LH1, HL1, HH1, thin edges are gathered. Thin edges are one pixel thick in the three directional levels of decomposition: horizontal, vertical and diagonal. Component LL1 does not contain thin edges, thick edges remain and those in the source image I were several pixel thick. During the second decomposition, some verges will be located in fine components LH2, HL2, HH2, but the coarsest will remain in LL2. In this way the energy of coarse components decreases, and gets transferred to fine components. Thicker and thicker verges go to fine components. They also have higher contrast. Thus relative variances of details should gradually grow.
And what will happen if the source image I is disturbed by random noise of small variance, thus difficult to detect by a human eye? Random noise can be compared to short, point edges, having a small contrast compared to the surroundings. Such weak and thin edges should be reproduced in fine components at the first resolution level. Thus the variance of these components will be high, higher than for the noiseless image. The influence of noise should concentrate on the first resolution level and disappear on the
3. Practical Study and Results
In the studies the applied images came from the archives of the company MGGP AERO from Tarnow, Poland.
The company now possesses three cameras, one analogue, used sporadically and two digital ones.
The images were selected from the abundant archives of the company in the way that:
? they presented the same area;
? they have similar scale (similar GSD) and similar orientation to the north;
? they were taken at similar situation of the Sun;
? they were taken in small time intervals (also images from different years, but the same season were accepted).
The main characteristic of the used cameras are described below:
Analogue camera:
? camera type LMK1000 (Zeiss Jena);
? lens type LAMEGON;
? focal length 153 mm;
? film: AGFA Aviphot Color X100, developing process: C-41;
? scanner: DELTA SCAN, scanning resolution: 12μm and 14 μm.
First digital camera:
? camera type: DMC I, 100 MPixel (Z/I Imaging);
? focal length 120 mm;
? pixel size: 12 μm.
Second digital camera:
? camera type: DMC II, 230 MPixel (Z/I Imaging);
? focal length 92 mm;
? pixel size: 5.6 μm.
All these 10 pairs of images were taken from the archives of the company MGGP AERO and represented different scales and type of landscape. One image was taken with LMK camera and the other with DMC I or DMC II. The resolution of images ranged from high (GSD = 0.1 cm) to small (GSD = 0.5 m). All the source images were written in TIFF without compression (waste compression is source of quasi-random noise). In every image 5 areas of 1024 ×1024 pixel were selected, from which each was treated as separate image and subdued to wavelet transformation. Altogether the study material included 50 statistic samples, consisting of one image from the analogue camera and one from digital camera. This material is clearly extended in the relation to earlier studies of the authors [6].
An example of pair in big and small scale is showed in Figs. 3 and 4, respectively.
Prior to the analysis of noise content, coloured images were replaced with a resultant luminance image, using equation:
carried out on three resolution levels (R = 3). Then the behavior of Eq. (5) components was analyzed. In particular we examined if the curve connecting the variance of details fulfilled the condition contained in Eqs. (6a) or (6b).
Comprehensive approach to the results is presented in Fig. 5. In all the studied cases, the increase was observed, but the inclinations were different. Thus in Fig. 5, the areas of the localizing the curves were shown, but not the individual curves. Different inclinations individual curves are connected with the influence of the structure and texture of the image (they depend on the land use and scale of the images) on the dynamics of equation components (5). However, more important than the inclination is the growing trend of the variance. The only disturbance of this trend occurred in the situation when the image contained predominantly lakes or other water bodies. The results from the images from the analogue camera were different. In this case the curve always falls between the first and second resolution level and then grows. The field in which all the curves for the images from the analogue camera were located were marked with hatching.
To clarify, one should underline that in Fig. 5, to increase the legibility, the variance of the last coarse component was not shown (compared with Fig. 2).
4. Conclusions
The analysis of the course of the equation of relative variance, during wavelet decomposition (5), turned out to be an efficient method of random noise detection. The low level of noise is indicated by stable growth of the variance of details, which takes place with the growth of decomposition level. This method does not show strong correlation with a natural fine-grain structure (typical of woodlands), which is a disadvantage of the method of detecting noise based on the shape of the distribution of wavelet fine components [3-5].
The comparison of the images from the analogue and digital camera confirmed clear difference in the content of random noise in favour of the digital camera, which contains definitely less noise. Such a conclusion was expected, because direct digital recording eliminates many sources of noise, occurring while taking digital images by scanning analogue images. The studies didn’t deal with the question what caused high noise level in the images recorded on the silver material and transformed into digital form by scanning. It was more important to confirm that the images from photogrammetric digital cameras contain small level of noise. This does not mean that there is no need to control the quality of such images.
The presented method is very suitable in comparing the level of noise between different images taken in the same area and in similar atmospheric and lighting conditions. The method does not measure the quantitative values of noise, it can only react to high level of noise. This results from the fact that on the course of curve illustrating equation of the course of variance (5) the structure and texture of image has also certain influence. Its variability does not disturb this growing trend of variance for subsequent levels of resolution, just the influence on the inclination of the curve. It is however possible to apply this method in quantitative assessment of noise in airport with aeroplanes used in photogrammetric flights (like in field tests for the geometric calibration of photogrammetric cameras).
Acknowledgments
The investigation has been made within the scope of research project AGH 11.11.150.949.
References
S.A. Morain, V.M. Zanoni, Joint ISPRS/CEOS-WGCV task force on radiometric and geometric calibration, in: ISPRS Congress, Istanbul, 2004, pp. 354-360.
S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 1998.
E.P. Simoncelli, E.H. Adelson, Noise removal via Bayesian wavelet coring, in: Proceedings of 3rd IEEE International Conference on Image Processing, Lausanne,
Switzerland, 1996, Vol. 1, pp. 379-382.
E.P. Simoncelli, Modeling the joint statistic of images in wavelet domain, in: Proc. SPIE 44th Annual Meeting, Denver, Colorado, 1999, Vol. 3813, pp. 188-195.
K. Pyka, Valorization of the noise content in photogrammetric images using wavelets, Geomatics and
2. MGGP AERO Company, Tarnow 33-100, Poland
Received: July 4, 2011 / Accepted: August 5, 2011 / Published: February 20, 2012.
Abstract: The paper presents the method of the valuation of random noise in the photogrammetric images, based on wavelets. The proposed method involves the analysis of the dynamics of the components of wavelet decomposition on several resolution levels. The hypothesis was made that the noise-free images are characterized by systematically growing variances of the single components with growing decomposition. This hypothesis was studied on several dozen fragments of airborne images recorded both with a photogrammetric analogue camera and digital camera. For all the studied photos taken with a digital camera, the hypothesis of growing variances of details was confirmed. The images from an analogue camera had different dynamics of variance, and the cause was recognized as random noise, caused by the grains from of the photographs. Referring to earlier applications of wavelets to noise evaluation, the proposed method is characterized by smaller dependence upon the structure and texture of the image.
Key words: Noise, camera, wavelets transform, decomposition, variance.
1. Introduction
When at the ISPRS Congress in Amsterdam, in 2000, the companies of Leica and Z/I Imaging showed the prototypes of first photogrammetric digital cameras, few people believed that within one decade the analogue cameras would be changed into digital ones. In those times people thought that photogrammetric technology, based on analogue photographs taken by cameras that had been improved for years, then scanned and converted into a digital form, did not need new solutions. Yet the images from digital frame cameras had at first much smaller size than those that could be achieved by scanning analogue images. The problem of the smaller size of the image from a digital camera has not been solved yet, but now it is not as significant as it was in the first cameras. Let’s notice that an analogue image of 23 cm × 23 cm, scanned with the resolution 2000 dpi, has the size of about 325 Mega pixels, while the image from the newest digital camera DMC II by Z/I Imaging is of 250 Mega pixels. Thus, in terms of the size the images of the photogrammetric digital camera have not been made equal to the scanned analogue images, yet. So why analogue cameras of air borne photogrammetry are now used only sporadically and mainly digital cameras are used?
The answer to the above question is much better radiometric quality of images taken by digital cameras. A better radiometric quality not only does improve the quality of the ortho-photomap, making the most popular photogrammetric product, but—what is more important—allows higher level of the automatication of the technological process. The application of images from digital cameras accelerates the process of aero-triangulation and the creation of the digital terrain model (DTM).
One of the elements of radiometric quality, apart from radiometric resolution, contrast and tonal
matching, is the noise level in the image. Noise can be defined as a signal, which is unfavourable, appears accidentally or systematically and disturbs the image diminishing its information value [1]. In the case of scanned analogue images, the main source of random noise is coarse photographic emulsion and instability of the scanner’s detectors. The image taken by a digital camera can contain random noise arising during the formation of the image during the process of sampling, coding, compression and transmission of the image.
The article proves that images taken with an analogue camera and then scanned contained much higher level of noise than images taken with a digital camera. As a tool of studying noise in the images, wavelet transformation was applied.
2. The Application of Wavelet Transformation for the Detection of Noise in the Images
Wavelet transformation is replacing the classical record of the image as a spatial function of 2D space. It is a frequency-spatial representation of the image. The method of marking developments of wavelet images with the multi-stage decomposition, using one-dimension filters were applied separately for verses and columns of the image, given by Mallat [2]. In the wavelet development of image I four components occur: one so-called coarse (LL) and three detail, defined as vertical (LH), horizontal (HL) and diagonal (HH). The characteristic feature of wavelet transformation is the possibility of its continuation in the relation to the selected components, which usually better develops the coarse component (such a scheme was accepted in the study). Fig. 1 presents the classic scheme of image wavelet decomposition according to Mallat [2]. This scheme was used in these studies. Every subsequent image wavelet decomposition consists of four components half a size (in linear terms). For example if the size of the original image is 1024 × 1024 pixel, the size of all the four components on the first resolution level is 512 × 512, on the second 256 × 256, etc..
The application of wavelet image representation in the assessment of the image radiometric quality was first proposed by Simoncelli [3, 4], who noticed that the distribution of the wavelet coefficients of detail components shows sharp maximum in point zero and good symmetry, while the flattening of the histogram is correlated with the presence of noise in the image. However, this method is not objective, because the results are strongly influenced by the structure and texture of the image [5].
One of the properties of wavelet transformation is preserving the energy of the image during its decomposition [2]. In case of decomposition, on one resolution level it obtains:
E(I)?E(LL1)?E(LH1)?E(HL1)?E(HH1)(1) where:
E(I) = energy of image I;
E(LL1) = energy of coarse component LL on first level of decomposition;
E(LH1), E(HL1), E(HH1) = energy of detail components LH, HL, HH (on the first level of decomposition).
Further decomposition of coarse detail is written
From Eq. (5), it can be concluded that the sum of the variances of wavelet components normalized by the variance of the image equals 1. It is worth emphasising that one of the variables of Eq. (5) is the level of decomposition R, which means that the sum of the variances of wavelet components is the same for each wavelet development of the image. Fig. 2 shows graphic interpretation of Eq. (5), assuming two things:
? The number of decomposition levels R = 3;
? The curve combining two subsequent values of variance is growing.
The first assumption is arbitrary, a relatively small number of decomposition levels was selected, but was sufficient for detecting the trends in variance changes. The second assumption is a study hypothesis, which has to be explained. Wavelet transformation according to the Mallat scheme is a combination of low-pass and high-pass filtration, with simultaneous dyadic reduction of the image size (Fig. 1). The idea of every decomposition is localizing the selected edges (places where the brightness changes) of the image in fine components and leaving the remaining image information in the course component. On the first level in components LH1, HL1, HH1, thin edges are gathered. Thin edges are one pixel thick in the three directional levels of decomposition: horizontal, vertical and diagonal. Component LL1 does not contain thin edges, thick edges remain and those in the source image I were several pixel thick. During the second decomposition, some verges will be located in fine components LH2, HL2, HH2, but the coarsest will remain in LL2. In this way the energy of coarse components decreases, and gets transferred to fine components. Thicker and thicker verges go to fine components. They also have higher contrast. Thus relative variances of details should gradually grow.
And what will happen if the source image I is disturbed by random noise of small variance, thus difficult to detect by a human eye? Random noise can be compared to short, point edges, having a small contrast compared to the surroundings. Such weak and thin edges should be reproduced in fine components at the first resolution level. Thus the variance of these components will be high, higher than for the noiseless image. The influence of noise should concentrate on the first resolution level and disappear on the
3. Practical Study and Results
In the studies the applied images came from the archives of the company MGGP AERO from Tarnow, Poland.
The company now possesses three cameras, one analogue, used sporadically and two digital ones.
The images were selected from the abundant archives of the company in the way that:
? they presented the same area;
? they have similar scale (similar GSD) and similar orientation to the north;
? they were taken at similar situation of the Sun;
? they were taken in small time intervals (also images from different years, but the same season were accepted).
The main characteristic of the used cameras are described below:
Analogue camera:
? camera type LMK1000 (Zeiss Jena);
? lens type LAMEGON;
? focal length 153 mm;
? film: AGFA Aviphot Color X100, developing process: C-41;
? scanner: DELTA SCAN, scanning resolution: 12μm and 14 μm.
First digital camera:
? camera type: DMC I, 100 MPixel (Z/I Imaging);
? focal length 120 mm;
? pixel size: 12 μm.
Second digital camera:
? camera type: DMC II, 230 MPixel (Z/I Imaging);
? focal length 92 mm;
? pixel size: 5.6 μm.
All these 10 pairs of images were taken from the archives of the company MGGP AERO and represented different scales and type of landscape. One image was taken with LMK camera and the other with DMC I or DMC II. The resolution of images ranged from high (GSD = 0.1 cm) to small (GSD = 0.5 m). All the source images were written in TIFF without compression (waste compression is source of quasi-random noise). In every image 5 areas of 1024 ×1024 pixel were selected, from which each was treated as separate image and subdued to wavelet transformation. Altogether the study material included 50 statistic samples, consisting of one image from the analogue camera and one from digital camera. This material is clearly extended in the relation to earlier studies of the authors [6].
An example of pair in big and small scale is showed in Figs. 3 and 4, respectively.
Prior to the analysis of noise content, coloured images were replaced with a resultant luminance image, using equation:
carried out on three resolution levels (R = 3). Then the behavior of Eq. (5) components was analyzed. In particular we examined if the curve connecting the variance of details fulfilled the condition contained in Eqs. (6a) or (6b).
Comprehensive approach to the results is presented in Fig. 5. In all the studied cases, the increase was observed, but the inclinations were different. Thus in Fig. 5, the areas of the localizing the curves were shown, but not the individual curves. Different inclinations individual curves are connected with the influence of the structure and texture of the image (they depend on the land use and scale of the images) on the dynamics of equation components (5). However, more important than the inclination is the growing trend of the variance. The only disturbance of this trend occurred in the situation when the image contained predominantly lakes or other water bodies. The results from the images from the analogue camera were different. In this case the curve always falls between the first and second resolution level and then grows. The field in which all the curves for the images from the analogue camera were located were marked with hatching.
To clarify, one should underline that in Fig. 5, to increase the legibility, the variance of the last coarse component was not shown (compared with Fig. 2).
4. Conclusions
The analysis of the course of the equation of relative variance, during wavelet decomposition (5), turned out to be an efficient method of random noise detection. The low level of noise is indicated by stable growth of the variance of details, which takes place with the growth of decomposition level. This method does not show strong correlation with a natural fine-grain structure (typical of woodlands), which is a disadvantage of the method of detecting noise based on the shape of the distribution of wavelet fine components [3-5].
The comparison of the images from the analogue and digital camera confirmed clear difference in the content of random noise in favour of the digital camera, which contains definitely less noise. Such a conclusion was expected, because direct digital recording eliminates many sources of noise, occurring while taking digital images by scanning analogue images. The studies didn’t deal with the question what caused high noise level in the images recorded on the silver material and transformed into digital form by scanning. It was more important to confirm that the images from photogrammetric digital cameras contain small level of noise. This does not mean that there is no need to control the quality of such images.
The presented method is very suitable in comparing the level of noise between different images taken in the same area and in similar atmospheric and lighting conditions. The method does not measure the quantitative values of noise, it can only react to high level of noise. This results from the fact that on the course of curve illustrating equation of the course of variance (5) the structure and texture of image has also certain influence. Its variability does not disturb this growing trend of variance for subsequent levels of resolution, just the influence on the inclination of the curve. It is however possible to apply this method in quantitative assessment of noise in airport with aeroplanes used in photogrammetric flights (like in field tests for the geometric calibration of photogrammetric cameras).
Acknowledgments
The investigation has been made within the scope of research project AGH 11.11.150.949.
References
S.A. Morain, V.M. Zanoni, Joint ISPRS/CEOS-WGCV task force on radiometric and geometric calibration, in: ISPRS Congress, Istanbul, 2004, pp. 354-360.
S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 1998.
E.P. Simoncelli, E.H. Adelson, Noise removal via Bayesian wavelet coring, in: Proceedings of 3rd IEEE International Conference on Image Processing, Lausanne,
Switzerland, 1996, Vol. 1, pp. 379-382.
E.P. Simoncelli, Modeling the joint statistic of images in wavelet domain, in: Proc. SPIE 44th Annual Meeting, Denver, Colorado, 1999, Vol. 3813, pp. 188-195.
K. Pyka, Valorization of the noise content in photogrammetric images using wavelets, Geomatics and