Fast correlation technique for glacier flow monitoring by digital camera and space-borne SAR images
© Vernier et al; licensee Springer. 2011
Received: 17 October 2010
Accepted: 28 September 2011
Published: 28 September 2011
Most of the image processing techniques have been first proposed and developed on small size images and progressively applied to larger and larger data sets resulting from new sensors and application requirements. In geosciences, digital cameras and remote sensing images can be used to monitor glaciers and to measure their surface velocity by different techniques. However, the image size and the number of acquisitions to be processed to analyze time series become a critical issue to derive displacement fields by the conventional correlation technique. In this paper, a mathematical optimization of the classical normalized cross-correlation and its implementation are described to overcome the computation time and window size limitations. The proposed implementation is performed with a specific memory management to avoid most of the temporary result re-computations. The performances of the software resulting from this optimization are assessed by computing the correlation between optical images of a serac fall, and between Synthetic Aperture Radar (SAR) images of Alpine glaciers. The optical images are acquired by a digital camera installed near the Argentière glacier (Chamonix, France) and the SAR images are acquired by the high resolution TerraSAR-X satellite over the Mont-Blanc area. The results illustrate the potential of this implementation to derive dense displacement fields with a computational time compatible with the camera images acquired every 2 h and with the size of the TerraSAR-X scenes covering 30 × 50 km2.
In the last decades, the warmer climate, together with less precipitation in the glacial accumulation areas, has resulted in a spectacular retreat of most of the monitored temperate glaciers . If confirmed in the coming years, this evolution will have important consequences in terms of water resources, economical development and risk management in the surrounding areas. To monitor glacier displacements and surface evolutions, two main complementary sources of information are available:
in-situ data collected for instance using accumulation/ablation stakes, Global Positioning System (GPS) stations, or digital cameras installed near the glaciers to acquire regular images of specific areas such as serac falls, unstable moraines ...
remote sensing data acquired by air-borne or space-borne sensors such as multispectral optical images or Synthetic Aperture Radar (SAR) images.
Optical data sets are often used to observe changes and allow the computation of high resolution (HR) information such as the surface elevation or glacier displacement fields during the summer [2–4], but they cannot be regularly acquired along the year and efficiently used because of clouds or snow cover uniformity. Space-borne SAR data, especially the recently lunched HR satellites such as TerraSAR-X, COSMO-SkyMed or Radarsat-2, are a new source of information which may allow global evolution monitoring and provide regular measurements thanks to the all-weather capabilities of SAR imagery. They are used to derive surface changes and velocity fields , or to detect and track rocks and crevasses .
With the increase of the sensor spatial resolution, the data transmission and storage possibilities, the use of image time series for Earth observation is facing computational challenges which can be separated into two groups: the need to develop new signal/image processing methods to extract information from huge amount of data, but also the need to improve existing robust techniques applied at the early processing stages to be able to apply them in a reasonable computation time on very large images and on large number of images to explore temporal evolution. Image co-registration is one of the first tasks to be performed to handle time series of images acquired by a sensor in similar conditions. When motion-free areas and moving features can be distinguished, this co-registration stage also provides displacement information which is useful to derive surface displacement fields. This task is often performed by the well-known correlation technique, which can be applied in different ways.
Several tools have been developed to solve the classical correlation problem. For optical imagery, a software like Co-registration of Optically Sensed Images and Correlation (COSI-Corr) [7, 8] is widely used in the geoscience community. Due to its integration to ENVI, COSI-Corr is easy to use and offers classical and Fast Fourier Transform (FFT) techniques to compute correlation. However, its use for large images is limited by computation time. For SAR imagery, the well-known software called Repeat Orbit Interferometry Package (ROI-PAC)  is dedicated to SAR interferometry, but it also includes tools to solve the amplitude correlation problem. A two steps strategy has been adopted: a first global co-registration of the two images on a sparse grid, followed by the refined computation of the correlation on a regular grid. A disadvantage of ROI-PAC is that the computation time can dramatically increase with the image size and the number of correlation points in the image.
There are many different techniques developed for image co-registration [10, 11]. Those based on sub-image correlation operate either in the temporal domain (the spatial domain for the 2 dimensional (2D) signal images) by directly computing the values of the cross-correlation function and searching for its peak, or in the spectral domain after the computation of the discrete Fourier transform of the two sub-images. The methods developed in the spectral domain are meant to speedup the computation using the FFT algorithm proposed with optimized implementation in signal/image processing libraries . They derive the sub-image shift either from the phase of the cross-spectrum , or by computing its inverse Fourier transform and identifying the correlation peak in the spatial domain . A basic computation of the cross-correlation in the spatial domain requires a number of operations proportional to N2, whereas with an implementation in the spectral domain, it is proportional to N log N. A speedup of the process is expected when the window size increases, with the constraint of being a power of 2 in both directions to benefit from the FFT optimizations.
Compared with the conventional implementation of the correlation in the spatial domain, the benefit of the spectral approach depends on the window sizes. An efficient implementation in the spatial domain also presents some advantages. It is more flexible since there is no constraint on window sizes, which allows the limitation of the local stationarity hypothesis to be taken into account. It has also the advantage of being more generic since it allows the choice of different similarity criteria according to the statistics of the images. Several alternatives to the conventional "cross-correlation function" have been proposed for image co-registration , especially in the case of SAR images which are affected by the speckle effect for distributed targets. The properties of the "true correlation function" in the Fourier domain cannot be transposed for more complex criteria derived for instance from a maximum likelihood approach [16, 17].
In this paper, an implementation strategy of the correlation function in the spatial domain is proposed. The objective is to preserve the flexibility and the genericness of the spatial domain approach, and to benefit from the computation efficiency of parallel or distributed processing architectures which become more and more common on conventional computers. The originality of this approach is to be able to efficiently compute the disparity measure at the initial resolution and to derive a dense displacement field. To our knowledge, it is difficult to find efficient tools for such fast computation over large remote sensing images, whereas they are essential to manage the new data sets from HR sensors, time series and large scenes. The potential and the performances of this approach are illustrated on two kinds of data: remote sensing data with repeated pass acquisitions of HR TerraSAR-X images over fast moving glaciers in the Alps, and proximal sensing image time series from a digital camera installed in front of a serac fall of the Argentière glacier in the Mont-Blanc area.
This paper is organized as follows: Section 2 details the Normalized Cross-Correlation (NCC) algorithm, its optimization and its implementation, so as to obtain an efficient correlation software. In the next sections, Sections 3 and 4, the correlation software is applied to a realistic problem. Section 3 is dedicated to the computation of the displacement of serac falls in front of the Argentière glacier. The results show a set of serac displacements and highlight the impacts of the optimized software. Section 4 illustrates the computation of glacier flow by correlation of SAR images. This section confirms the results obtained with optical images and shows the impact of the master window size on the computation time. Finally, Section 5 concludes this paper and projects future work.
2 Implementation techniques for fast correlation
2.1 Similarity function
The correlation result is the computation of for all (k, l) such that and . Thus, for each point, the result is defined by and . The values of are, respectively, the displacement on the lines and the displacement on the columns of the point (k, l), and is the cross-correlation level for these displacements, which varies between 0 and 1.
2.2 Optimized algorithm
To optimize the algorithm and to reduce the computation time, the correlation algorithm must be rewritten to highlight the computation dependencies. The first objective is to avoid re-computing an already computed value. The second one is to introduce a flow computation technique to reduce the number of operations of the algorithm. These two techniques are the well-known summed-area tables algorithms . They have been more recently used in the method proposed by Viola and Jones  for object fast detection. According to these points, the correlation equations given in Section 2.1 can be rewritten as follows:
If k ≠ k0 the same optimizations--Equations 5-11--can be performed using the line dependencies.
Let us note that this optimization strongly reduces the number of operations compared with a naive implementation. As the number of operations is one of the most critical criteria for the efficiency, the correlation algorithm must be implemented according to this optimization.
For the implementation, one of the main problems is the memory to be used. The input and output images can be too big to be stored in the memory, and hard drive access can be very time consuming. Moreover, the optimizations presented in Section 2.2 need memory to store the precomputed values. Thus, an important point is to manage the required memory according to the available memory to execute the correlation algorithm as fast as possible.
The optimizations presented in Section 2.2 can be applied using line dependencies or column dependencies. Both are necessary. In our case, a point that is not on the first column is computed depending on the point on the previous column. A point that is on the first column, except on the first line, is computed depending on the previous line. In this way, the memory corresponding to the pre-computation of two points must be allocated, one for the next point on the same line and one to start the next line.
The required memory to compute the correlation can be greater than the available memory. That is why the implementation of the algorithm must manage the computation lines block. This kind of implementation has two advantages. First, it allows the distribution of the algorithm. If N Central Processing Units (CPU) are available, the images can be split in N blocks and each CPU computes the correlation on its block. Second, if on a machine there is not enough memory to compute the correlation, the implementation computes on a first block that can be stored in the memory, saves the results and then computes the next block, and so on.
This approach can be realized due to the fact that the needed memory for each part of the algorithm can be predicted according to the previous optimizations.
This optimized implementation is available in the Extraction and Fusion of Information for ground Displacement measurements with Radar Imagery (EFIDIR) Tools under GNU General Public License (GPL). These tools can be downloaded from the EFIDIR web site (see Acknowledgments).
3 Experiments and results on digital video camera images
In this section, the performances of the implementation proposed in Section 2 are assessed and illustrated on the processing of optical images from a digital camera installed for glacier monitoring. In the literature, two types of cameras have been used to measure glacier flow: the analog and the digital cameras. Initially, the traditional analog technology has been used in [20–23]. At the beginning of the twenty-first century, digital photography development has made the glacier flow monitoring with HR digital cameras possible. Up to now, only few experiments have been reported with HR digital cameras, as for example in Greenland polar glaciers [24, 25]. To our knowledge, no experiment on an Alpine temperate glacier has been performed.
3.1 Digital camera data set
Cameras installed around the Mont-Blanc massif
Autumn 2007 and Summer 2008
Mer de Glace
Tacul glacier (the Géant seracs falls)
The HR-automated digital cameras installed around the Mont-Blanc massif are based on customized Leica DLux 3 and DLux 4 units. They have been heavily modified to allow a custom low-power microcontroller-based board to control any basic function, including switching on and off the camera, focusing and triggering the shutter. When the user-defined alarm condition is met, the camera triggering sequence is started and a pre-defined amount of time is provided for the camera to focus and grab the picture before power is switched off to save battery life. All functions provided by the camera manufacturer for operator handling are simulated through analog switches. A custom software allows the user to define on the field the wake up hour, time interval between images and number of images taken every day. The default configuration is to wake up at 8 a.m. local time and grab six images every day, with 2 h intervals between images.
The system grabs 16:9 HR images of 10 Mega pixels (4, 224 × 2, 376 pixels) with the same field of view over time. The angle of view of the camera is calibrated to 65°, with a width of 4,224 pixels, the angle of view of a single pixel is 0.015° (aperture angle) .
All the images are stored as HR JPEG images: this format was selected as a compromise between storage efficiency (since the cameras are running autonomously for up to 6 months without supervision) and data quality. However, the JPEG format is not compatible with the mono-band fast correlation approach presented in this paper. Moreover, the weather conditions are often extreme above 2, 000 m ASL in mountain areas such as the Alps. Wind and strong temperature variations might move the camera, as observed previously on a similar setup . In such a case, a translation, up to 4 pixels in both directions, can be observed between two images.
- 1.The initial RGB JPEG images Ijpeg are converted in grayscale images Igray to obtain mono-band images. This conversion is processed according to the following formula:
An initial co-registration between the images is made on the motion-free part of the images. In practice, the motion-free parts, i.e. mountains on the background, are used to perform it. This initial image co-registration on motion-free areas is realized by a translation without applying sub-pixel offsets.
The proposed fast correlation technique is applied on the image pair with 31 × 31 pixels master window (i.e. Mr × Mc) and 51 × 51 pixels slave window (i.e. Sr × Sc), corresponding to a maximum offset of 10 pixels in each direction. On motion-free areas, the sub-pixel offsets provide an accurate estimation of the remaining offset due to the camera instability. On the glacier, the measured offset is the sum of the displacement offset and the geometrical offset which has not been compensated for at step 2.
3.3 Computation speedup
From Figure 7, the relative gain can be considered constant for our experiment and it is very significant: more than 96%. Since the computation without optimization can be very long--more than 1 day--the absolute gain can change the work habits. The prospects with many days of computation are not the same as with a few hours. The computation time and the absolute benefit decrease when the number of used CPU increases, but even with 8 CPU, several hours are saved thanks to the optimization.
This first experiment highlights the benefit of the optimization and the distribution of the correlation algorithm for optical images. It is important to note that this benefit enables to decrease the interval between two image captures. Consequently, a real time glacier flow monitoring becomes feasible. With the appropriate computation system, an acceleration of the glacier and an important loss of correlation corresponding to serac falls can be quickly detected.
4 Experiments and results on SAR images
Despite improved acquisition, transmission and processing performances, the proximal sensing by ground-based optical cameras, as illustrated in Section 3, is limited to specific parts of a few glaciers. In this section, the proposed fast correlation technique is applied to remote sensing data which can cover large areas: space-borne images allow the whole glacier surface, and even all the glaciers of a mountain area, to be observed simultaneously. The feasibility in a reasonable computation time and the interest of the dense correlation measurements of this fast correlation technique are illustrated on HR SAR images which can be regularly acquired by repeated satellite passes.
4.1 TerraSAR-X data set
Temporal series of TerraSAR-X images acquired on the Cha-monix Mont-Blanc test site.
No. of images
2007-10-24 to 2007-11-04
HH and HH/VV
Descending 5h44 UTC
1 pair with Δt = 11 days
Descending 5h44 UTC
Ascending 17h25 UTC
2008-09-29 to 2008-10-21
Descending 5h44 UTC
2 pairs with Δt = 11 days
2009-01-06 to 2009-03-24
Descending 5h44 UTC
7 pairs with Δt = 11 days
2009-05-29 to 2009-08-25
Descending 5h44 UTC
5 pairs with Δt = 11 days
2009-05-31 to 2009-08-27
Ascending 17h25 UTC
8 pairs with Δt = 11 days
2009-09-18 to 2009-10-21
Ascending 17h25 UTC
3 pairs with Δt = 11 days
In the mountainous areas where most of the Alpine glaciers are located, the "range sampling" of SAR images introduces strong geometrical distortions. To avoid geocoding artifacts, the SAR images of the Mont-Blanc test site have been ordered in their initial geometry. The offsets measured in range direction between two images are sensitive to the position along the swath (near range a /far range b ), to the topography, as well as to the surface displacement occurred between the two acquisition dates. The offsets measured in azimuth direction mainly depend on the surface displacement (a linear correction is sufficient to remove along-track registration variations over long scenes). The range variations due to the topography depend on the perpendicular baseline between the two orbits as in a stereo configuration. These variations can be predicted using a Digital Elevation Model (DEM) of the area and the orbital data (antenna state vectors) which are provided together with the images.
In the studied area, the altitude varies between 1,000 m ASL (in the Chamonix valley) up to 4,800 m ASL (on the Mont-Blanc). For the image pair (2008-09-29/2008-10-10) whose perpendicular baseline is around 138 m, the range registration offsets due to this baseline vary between 28.9 and 82.4 pixels in near and far range, respectively. The glaciers of this test site might move up to 1.5 m per day in the fastest areas, according to in situ measurements. The glacier displacements vary between 0 and 16 m in 11 days, hence 0-8 pixels with the resolution of the TerraSAR-X images used in this paper.
An initial co-registration by a simple translation (without resampling) is applied by matching an area of the image located at an intermediate elevation of about 2,000 m ASL.
The proposed fast correlation technique is applied to the whole image with 61 × 61 pixels master window (i.e. Mr × Mc) and 77 × 77 pixels slave window (i.e. Sr × Sc), corresponding to an offset of ±16 m in each direction. On motion-free areas, the sub-pixel offsets provide an accurate estimation of the remaining offset due to the SAR geometry. On the moving glaciers, the measured offset is the sum of the displacement offset and the geometrical offset which has not been compensated for at step 1.
Depending on the variations of the geometrical offset along the glaciers, a post-processing step can be necessary to deduce the offsets only due to the glacier movement. The remaining geometrical offset can be subtracted using either the predictions from the DEM and the orbits, or the results of the sub-pixel correlation around the glaciers.
4.3 Computation speedup
The relative gain is close to that obtained with the optical images: more than 96%. As the computation time without optimization is very long--many days--in the case of SAR images, the benefit can be expressed in computation days. Thus, the impacts of the optimization and distribution for SAR images are more important than for the smaller images of the digital camera.
Let us note that the absolute gain increases with the master window size and several hours are saved. It is also important to note that the relative gain increases with the size of the master window. In other words, the larger the master window size, the more efficient the optimization.
5 Conclusions and future work
This paper details an optimized implementation of the NCC algorithm. The objective is to reduce the computation time of the correlation technique to handle large data set for Earth change monitoring. The saved time induced by the optimization has multiple impacts. The computation on each point of the image can be achieved in a reasonable time: 0.02 min/mega pixel instead of 0.4 min/mega pixel with a conventional approach. High resolution remote sensing images covering large scenes can be processed in few hours. This fast correlation technique is very useful to extend experimental researches. For example, it allows researchers to experiment different processing parameters and to analyze large data sets.
Two experiments illustrate the benefits of the proposed approach. The evolution of serac falls is studied with optical images and the whole glacier surface evolution can be observed with SAR images. On the Mont-Blanc area, the correlation reveals particular areas like glaciers, lakes or other changing features that can be studied. These experimental results highlight the potential of proximally and remotely sensed images to monitor the glacier flow and to contribute to risk assessment: the Taconnaz glacier is for instance an important source of risk for the access road to the Mont-Blanc tunnel.
Future work includes a comparison between this optimization and different implementations of the FFT approach to illustrate the advantages and limitations of those techniques. Regarding the optical images, a stereo camera will be installed near Argentière glacier to measure simultaneously the topography and the displacement of the serac fall. Regarding the SAR images, as the NCC is only one of the available similarity functions, the study and the optimization of new criteria, different from the NCC, will also be investigated.
The authors wish to thank the French Research Agency (ANR) for supporting this work through the Hydro-Sensor-FLOWS project and the EFIDIR project (ANR-2007-MCDC0-04, http://www.efidir.fr). They also wish to acknowledge the German Aerospace Agency (DLR) for the Terra-SAR-X images (project MTH0232) and Électricité Emosson SA for their support.
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