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 PowerPoint PPT Presentation


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GLOBAL MOTION ESTIMATION OF SEA ICE USING SYNTHETIC APERTURE RADAR IMAGERY. Mani V. Thomas. Problem Statement. 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

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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

GLOBAL MOTION ESTIMATION OF SEA ICE USING SYNTHETIC APERTURE RADAR IMAGERY

Mani V. Thomas


Problem statement

Problem Statement

  • 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”


Introduction

Introduction

  • 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


Motion estimation problem

Motion Estimation Problem

  • “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


Motion estimation problem1

Motion Estimation Problem

  • 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


Motion estimation problem2

Motion Estimation Problem

  • 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


Motion estimation problem3

Motion Estimation Problem

  • 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


Fourier theory

Fourier Theory

  • 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


Fourier theory1

Fourier Theory

  • 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


Global motion estimation

Global Motion Estimation

  • 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


Global motion estimation1

Global Motion Estimation

  • 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


Global motion estimation2

Global Motion Estimation

  • 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


Global motion estimation3

Global Motion Estimation

  • 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

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


Global motion estimation4

Global Motion Estimation

  • 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


Global motion estimation5

Global Motion Estimation

  • 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

  • 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


Global motion estimation6

Global Motion Estimation

  • 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


Global motion estimation7

Global Motion Estimation

  • 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


Functional description of modules

Functional Description of Modules

  • 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


Data sets

Data Sets

  • 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


Data sets1

Data Sets

  • 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


Data sets2

Data Sets

  • 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


Results and analysis

Results and Analysis

  • 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


Results and analysis1

Results and Analysis

  • 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


Results and analysis2

Results and Analysis

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


Results and analysis3

Results and Analysis

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


Results and analysis4

Results and Analysis

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


Results and analysis5

Results and Analysis

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


Results and analysis6

Results and Analysis

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


Results and analysis7

Results and Analysis

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


Results and analysis8

Results and Analysis

  • 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


Results and analysis9

Results and Analysis

Comparison of 30585103 and 30685693: Turbulent zone


Results and analysis10

Results and Analysis

  • 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


Results and analysis11

Results and Analysis

  • 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


Conclusion

Conclusion

  • 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.

  • 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

Thank you


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