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GLOBAL MOTION ESTIMATION OF SEA ICE USING SYNTHETIC APERTURE RADAR IMAGERY

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GLOBAL MOTION ESTIMATION OF SEA ICE USING SYNTHETIC APERTURE RADAR IMAGERY

Mani V. Thomas

- Sea-Ice dynamics is composed of
- Large global translation
- Small local non-rigid dynamics

- Robust estimation of global motion provides a base for processing of non-rigid components
- “Given a pair of ERS – 1 SAR images, this thesis presents a method of estimating the global motion occurring between the pair robustly”

- Investigation into the robust estimation of the global motion of sea ice as captured by the European Remote Sensing Satellite (ERS) imagery.
- Reasons for estimation complexity
- Differences in the swaths of the satellite and the rotation of the earth
- the local sea-ice dynamics is over shadowed by the large magnitudes of the global translation

- Time difference between the adjacent frames (typically three days due to polar orbit constraints)
- Influence of fast moving storms
- Significant non-linear changes in the discontinuities occur at temporal scales much lesser than 3 days

- Differences in the swaths of the satellite and the rotation of the earth

- “Optic Flow is computed as an approximation of the image motion defined as the projection of the velocities of 3-D surface points onto the imaging plane” [Beauchemin, 1995]
- Image Brightness Constancy assumption
- Apparent brightness of a moving object remains constant [Horn, 1986]
- Under the assumption of extremely small temporal resolution the optic flow equation is considered valid

- Apparent brightness of a moving object remains constant [Horn, 1986]

- Estimation techniques can be classified into three main categories [Kruger, 1996]
- Differential methods [Horn, 1981] [Robbins, 1983]
- Image intensity is assumed to be an analytical function in the spatio-temporal domain
- Iteratively calculates the displacement using the gradient functional of the image
- work well for sub-pixel shifts but they fail for large motions
- extremely noise sensitive due numerical differentiation
- convergence in these methods can be extremely slow

- Differential methods [Horn, 1981] [Robbins, 1983]

- Area based methods [Jain, 1981], [Cheung, 1998]
- The simplest way in terms of both hardware and software complexity
- Implemented in most present day video compression algorithms [ISO/IEC 14496-2, 1998; ITU-T/SG15, 1995]
- Estimation is performed by minimizing an error criterion such as “Sum of Squared Difference”
- Not satisfied completely since motion in real life can be considered a collage of various types of motions

- Feature based methods
- Identify particular features in the scene
- computes the “feature points” between the two images using corner detectors [Harris, 1998; Tomasi, 1991]

- Deducing the motion parameters by matching the extracted features
- Matching the detected feature between the two images using robust schemes such as RANSAC [Fischler, 1981]
- Full optic flow is known at every measurement position
- Only a sparse set of measurements is available
- Reduction of the amount of information being processed

- Identify particular features in the scene

- Fourier Transform of Aperiodic signals
- Fourier Analysis equation
- Fourier Synthesis equation
- Fast Fourier Transform [Cooley, 1965]
- Reduces computation from to

- Fourier shift Theorem
- Delay in the time domain of the signal equivalent to a rotation of phase in the Fourier domain

- Phase Correlation
- Given cross correlation equation in Fourier Domain
- Inverse Fourier Transform of the product of the individual forward Fourier Transforms
- By the Fourier Shift Theorem in 2D

- Sharpening the cross correlation using and [Manduchi, 1993]
- Inverse Fourier Transform provide a Dirac delta function centered at the translation parameters

- Given cross correlation equation in Fourier Domain

- Generalized Aperture Problem
- Uncertainty principle in image analysis
- Smaller the analysis window, greater the number of possible candidate estimates
- Larger the analysis window size, the greater is the probability that the analysis window has a combination of various motions

- Handle the motion estimation at multiple resolutions
- Information percolation from coarser resolution to finer resolution in a computationally efficient fashion.
- Motion smaller than the degree of decimation is lost

- Uncertainty principle in image analysis

- Global translations, in ERS-1images, are on the order of 100 to 200 pixels
- “Normalized Cross Correlation” (NCC) or “Sum of Squared Distance” (SSD) require large support windows to capture the large translation
- Large support windows encompass a combination of various motions
- Images have varying degrees of illumination due to the degree of back scatter

- SSD is extremely sensitive to the illumination variation though computationally tractable
- NCC is invariant to illumination but is computationally ineffective

- Phase correlation is illumination invariant [Thomas, 1987]
- Characterized by their insensitivity to correlated and frequency-dependent noise

- Calculations can be performed with much lower computational complexity with 2-D FFT
- It can be used robustly to estimate the large motions [Vernon 2001] [Reddy, 1996] [Lucchese, 2001]
- Separation of affine parameters from the translation components [De Castro 1987] [Lucchese 2001] [Reddy 1996]

- Main disadvantage is applicability only under well-defined transformations

- Phase Correlation v/s NCC
- Uni-modal Motion distribution within the search window
- Phase correlation and NCC have maxima at the same position

- Multi modal motion distribution within search window
- NCC produces a number of local maxima
- Phase correlation produces reduced number of possible candidates

- Uni-modal Motion distribution within the search window

Remark: Basis for support in both methods have been maintained at 96 pixels window

- Histogram Equalization by Mid-Tone modification
- Image enhancement and histogram equalization performed over “visually significant regions” as against the entire image
- Simple histogram equalization suffers from speckle noise and false contouring [Bhukhanwala, 1994]
- Experiments indicate that estimated motion field had the smallest error variance under mid tone modification

- Creation of Image Hierarchy by Median Filtering
- Multi-resolution image hierarchy by decimation in the spatial scale [Burt, 1983]
- Aliasing due to the signal decimation
- Reduced using Median filtering

- Small motions tend to get masked during the process of image decimation
- Masking is advantageous for global motion estimation

- Aliasing due to the signal decimation

- Multi-resolution image hierarchy by decimation in the spatial scale [Burt, 1983]
- Motion Estimation in Image Hierarchy
- Motion estimated at the coarsest level of the pyramid
- Estimate is percolated to the finer levels in the pyramid by warping the images towards one another
- Process iterated until the finest level of the pyramid
- Reduces the computational burden since the coarse estimate is performed on smaller images

- Histogram based global motion Estimation
- Images divided into a tessellation of blocks, each block centered within a predefined window.
- Window size, Block size and pyramid levels obtained as a parameter from the end user

- Motion estimated at each block using phase correlation
- Potential candidates are selected such that their magnitudes are higher than a threshold
- The best possible estimate obtained from the potential candidates using the “Lorentzian estimator” [Black, 1992]
- The global motion at a level of pyramid is obtained as the mode of the motion vectors at that level

- Images divided into a tessellation of blocks, each block centered within a predefined window.

- Due to the periodic nature of the Discrete Fourier Transform, the maximum measurable estimate using the Fourier Transform of a signal within a window of size W is W/2.
- To capture translations of magnitude (u, v), the W should be >= 2*max(u,v)
- For the ERS-1 experimentation, the block size was taken as 32X32 and the window size was taken as 128X128.
- The sizes of the window and the block are maintained a constant throughout the entire pyramid hierarchy
- Amplification of the estimates at the finer level of the pyramid

- The first level image processing related functional units.
- The image reader reads the image into buffers
- The image modifier that performs histogram equalization
- Create image hierarchy

- The second level performs the global motion estimation
- Performs phase correlation on the image pyramid
- analyzer functional module performs histogram analysis of the motion data

- The final level performs local motion estimation
- Affine components of the local non rigid deformations or a higher order parametric model

- The European Space Agency’s ERS – 1 and ERS – 2 C-band (5.3 GHz) Active Microwave Instrument generate RADAR images of the Southern Ocean sea-ice cover in Antarctica, in particular the Weddell Sea
- Weather independent (day or night)
- Frequent repeat
- High resolution 100 km swath

- The 5 month Ice Station Weddell (ISW) 1992 was the only winter field experiment performed on the Western Weddell Sea.
- The orbit phasing of the ERS – 1 was fixed in the 3-day exact repeating orbit called the ice-phase orbit
- Uninterrupted SAR imagery of 100 x 100 km2 spatial coverage of during the entire duration of the experiment

Courtesy: http://www.ldeo.columbia.edu/res/fac/physocean/proj_ISW.html

- SAR images obtained from ERS -1 are projected onto the SSM/I grid
- For the SAR imagery in the Southern Hemisphere, the tangent plane was moved to 70oS and the reference longitude chosen at 0o

- Values are transformed to X-Y grid coordinates using polar stereographic formulae
- The digital images are speckle filtered to a spatial resolution of 100m
- Images with dimensions of 1536 pixels in the horizontal and vertical direction
- Specified using a concatenation of orbit number and the frame number

Courtesy: http://nsidc.org/data/psq/grids/ps_grid.html

- Validation Motion Vectors (Ground Truth JPL Motion Vectors)
- Motion vectors for each 100x100 km2 SAR images were resolved using a nested cross-correlation procedure [Drinkwater, 1998] to characterize 5x5 km2 spatial patterns.
- A total of 12 such image pairs exist from this processing with an RMSE of less than 0.5 cm/s

- The code for performing the motion field estimation has been written C (VC++ 6.0) with the validation prototype written in Matlab 6.1 (R12).
- Window size is chosen a power of 2
- Maximize the throughput of the FFT modules,

- The block size adjusted at 8x8, 16x16 or 32x32 depending on the spatial resolution
- Output motion field at 0.8 km, 1.6 km or 3.2 km resolution.

- Estimated motion field in the images below have been computed using a 32x32 block size and a 128x128 window size
- These are overlaid on the JPL vectors on a 5km grid in the SSM/I coordinates, using linearly interpolation

- Two statistical measures of the similarity have been computed for the magnitude and the direction
- Root Mean Square Error
- Index of agreement [Willmott,1985]
- where pk are the estimated samples, ok are the observed samples (ground truth vectors), wk are the weight functions

Comparison of 34025103 and 34125693: estimated vectors v/s JPL vectors

Comparison of 30585103 and 30685693: estimated vectors v/s JPL vectors

Comparison of 31115693 and 31445103: estimated vectors v/s JPL vectors

Comparison of 31445103 and 31545693: estimated vectors v/s JPL vectors

Comparison of 32305103 and 32835693: estimated vectors v/s JPL vectors

Comparison of 31975693 and 32305103: estimated vectors v/s JPL vectors

- Motion estimation between the 31975693 and 32305103
- Block resolution of 4x4
- Observation of a turbulent field using higher resolution of analysis window

- Cluster map using a Quad-tree model
- Based on the variance of the magnitude and direction of the motion field

Comparison of 30585103 and 30685693: Turbulent zone

- Local Motion Analysis
- Simplest model of local motion
- Piecewise linear approximation of the non rigid motion using phase correlation

- Differential motion overlaid upon the correlation map of the goodness of the estimate
- Regions of low correlation provide the positions of discontinuities in the ice motion

- Simplest model of local motion

- False discontinuities due to projection of the non linear components, of the higher order motion, onto a linear motion space via phase correlation
- Abrupt changes in the frequency components cause abrupt variations in the estimated vector field

- Sub-pixel motion interpolation using a cubic spline.
- Within a window around the result of the local phase correlation, a cubic spline was fit and the peak of the spline so estimated was used as the sub-pixel motion estimate.
- This procedure reduced the bands of discontinuities within the motion field
- The main disadvantage is the computational burden of fitting a cubic slpine

- Within a window around the result of the local phase correlation, a cubic spline was fit and the peak of the spline so estimated was used as the sub-pixel motion estimate.

- Robust calculation of the motion occurring between two ERS-1 SAR sea-ice images
- Under the assumption that the net motion is composed of a large global motion component and small local deformations
- Phase Correlation provides a robust method to capture the large global motion component
- Inherent robustness to illumination variation
- Reduced computational burden due to FFT

- Having eliminated the global motion, estimate the local deformation using a higher order motion model such as an affine or a quadratic.

- Phase Correlation provides a robust method to capture the large global motion component
- Subsequent stage to the current research
- Improvement of local estimation from a simple piecewise linear approximation to using a robust higher order motion model
- Feature-based approaches to improve the overall robustness of the global motion estimates

Thank you