1. REMOTE SENSING Pre-Processing Radiometric Correction Geometric Correction
Professor Ke-Sheng Cheng
Department of Bioenvironmental Systems Engineering
National Taiwan University

2. Radiometric Correction
Detector error
Atmospheric effect
Dark Object Subtraction (DOS)
Multi-date Brightness Regression
Topographic effect
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

3. Radiometric Correction for Detector Error
If a detector of a n-detector scanning sensor system fails to function during a scan, it will result in a line of missing data. This is called the line drop-out problem.
If a detector does not fail completely, but just goes out of adjustment, it will result in n-line stripping.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

4. 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

5. Image Desrtipping x: uncorrected DN of the defect detector
y: corrected (destripped) DN of the defect detector
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

6. Radiometric Correction for Atmospheric Effect
Absolute radiometric correction
See the example of the previous subject.
It requires values of many atmospheric parameters at the time of overpass which may not be available to users.
Relative radiometric correction
Dark Object Subtraction (DOS)
Multi-date brightness regression
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

7. Dark Object Subtraction (DOS)
Also known as the Histogram Minimum Method (HMM).
The minimum scene radiance is set to be the upwelled-radiance based on the assumption that it represents the radiance from a scene element with near zero reflectance.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

8. For radiance reaching the sensor which corresponds to a waveband =2-1,
For a given sun-target-sensor geometry, only r is affected by the characteristics of the ground surface and the above equation can also be expressed by
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

9. Lmin, Lmax = the minimum and maximum measurable radiances of the sensor NG = number of grey levels used by the sensor system.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

10. The downwelled solar radiance is much smaller than solar irradiance and if it is neglected, it yields
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

11. If an image has been processed by the dark object subtraction method for atmospheric haze removal, then its DN is approximately a linear function of earth surface reflectance.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

12. Suppose that images of two different bands are available
Suppose that images of two different bands are available. If both images have been processed by HMM, then the ratio of their digital numbers is expressed as
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

13. Notice that cos is not present in the above equation and it explains why band-ratioing can suppress topographic shading if the haze removal is done first.
DOS only accounts for atmospheric scattering; the atmospheric absorption effect is not corrected.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

14. The last term on the RHS of the above equation is steady (does not vary with time).
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

15. Multi-date Brightness Regression
A set of regression equations that relate same-band brightness of target points (or radiometric control points, RCPs) present in multi-date images is developed.
The RCPs should be constant reflectors so that changes in their brightness values are attributed to detector calibration and atmospheric effects.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

16. 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

17. Each regression model contains an additive term (interception) that accounts for the difference in atmospheric path radiance between dates and a multiplicative term (slope) that accounts for the difference in detector calibration, sun-target-sensor geometry, and atmospheric transmittance between dates.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

18. Criteria for RCPs Selection
RCPs at be at approximately the same elevation as the other land within the scene.
RCPs should contain minimum amount of vegetation.
RCPs should be in a relatively flat area.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

19. Radiometric Correction for Topographic Effects
Topographic slope and aspect may introduce radiometric distortion of the recorded signal.
Removal of topographic effects should consider the slope and aspect of the individual pixels so that two objects (pixels) having the same reflectance properties shall show the same brightness value in the image despite their different orientation to the sun’s position.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

20. If the topographic slope-aspect correction is done very effectively, the three-dimensional impression of the corrected image shall be subdued.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

21. LT : radiance observed over slope terrain
LH : radiance observed for a horizontal surface (i.e., slope-aspect-corrected)
LT : radiance observed over slope terrain
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

22. The Cosine Correction 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

23. The cosine correction method only considers the direct solar irradiance that illuminates a pixel on the ground. It does not take into account diffuse sky irradiance (Ed).
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

24. The Minnaert Correction
In order to account for non-Lambertian surface reflectance, a Minnaert constant is introduced.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

25. Geometric Correction Applications: Three components:
correct system distortions
register multiple images
register image to map
Three components:
selection of suitable mathematical distortion model
coordinate transformation
resampling (interpolation)
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

26. Definitions for Geometric Correction
Registration: The alignment of one image to another image of the same area.
Rectification: The alignment of an image to a map so that the image is planimetric, just like the map. Also known as georeferencing.
Geocoding: A special case of rectification that includes scaling to a uniform, standard pixel GSI.
Orthorectification: Correction of the image, pixel-by-pixel, for topographic distortion.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

27. Example rectification of TM image
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

28. 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

29. THREE COMPONENTS TO WARPING
Appropriate mathematical distortion model(s)
Orbit model
Platform attitude model
Scanner model
Earth model
Coordinate transformation
Resampling (interpolation)
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

30. Orbit Model
The orbits of most earth remote sensing satellites are nearly circular. For precise modeling, an elliptical orbit may be assumed.
The orbit velocity of satellites can be considered constant in time
However, for airborne sensors, variation in platform attitude and ground speed cannot be assumed negligible.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

31. Platform Attitude Model
Platform attitude is critical to geometric precision because of the high altitude of remote sensing satellites or aircrafts.
Attitude of the sensor is characterized by three parameters:
Roll
Pitch
Yaw
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

32. Three attitude axes of a sensor platform
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

33. The actual values of roll, pitch and yaw are sampled and recorded with the image data. However, they are not always available to end users.
The spacecraft’s attitude does not vary in a systematic manner and can be modeled as a slowly changing function of time.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

34. The attitude variables a (representing roll, pitch and yaw) have been modeled as power series polynomials over time periods of several Landsat TM and SPOT images.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

35. Scanner Model
Scanner-induced geometric distortions are easy to account for because they can be described by mathematical functions.
As long as the scanner-induced distortions are consistent throughout an image and from orbit to orbit, they can be easily calibrated and corrected.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

36. Landsat MSS sensor Over-sampling in the cross-track direction.
Neighboring pixels have overlapping GIFOVs in the cross-track direction.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

37. Earth Model Earth rotational effect Panoramic effect
Earth curvature effect
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

38. Earth Rotational Effect
The earth rotates at a constant angular velocity, e. While the satellite is moving along its orbit and scanning orthogonal to it, the earth is moving underneath from west to east.
Since satellites such as Landsat and SPOT have an orbit inclination angle i (about 99) in order to achieve the desired revisit period and sun-synchronism, the earth rotation is not parallel to the cross-track scans.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

39. L = length of the image frame 0 = angular velocity of the satellite
e = Earth rotational (angular) velocity
ve = Earth surface velocity
 = latitude of the target pixel
re = Earth radius ( 106 m = 6378 km)
ta = Image acquisition time
 = offset distance on the earth surface
i = orbit inclination angle
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

40. 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

41. 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

42. The adjusted offset distance is
For Landsat or SPOT
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

43. Panoramic Effect
For scanners used on spacecraft and aircraft remote sensing platforms the angular IFOV is constant. As a result the effective pixel size on the ground is larger at the extremities of the scan than at nadir.
By placing the pixels on a uniform display grid the image will suffer an across track compression.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

44. Whisk-broom Sensor Panoramic Distortion (Horizontal Surface)
Across track distortion
Whisk-broom Sensor Panoramic Distortion
(Horizontal Surface)
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

45. The displacement for the pixel at the swath edge is
The cross-track displacement of a pixel can be determined by calculating the compression ratio
The displacement for the pixel at the swath edge is
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

46. In case of Landsat 1, 2, and 3,
This indicates that a pixel at the swath edge (92.5 km from the sub-nadir point) will be 314m out of position along the scan line compared with the ground if the pixel at nadir is in its correct location.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

47. Along track distortion
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

48. S-Band Distortion Whisk-broom Scanning Sensor 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

49. S-Band Distortion (only show cross-track distortion) 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

50. Panoramic Distortion of Whiskbroom Sensor (Horizontal Surface)
Cross track
Along track
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

51. Pushbroom Sensor Panoramic Distortion (Horizontal Surface)
Across track distortion
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

52. Across track distortion
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

53. Along track distortion
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

54. 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

55. Panoramic Distortion of Pushbroom Sensor (Horizontal Surface)
Cross track
Along track
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

56. Pushbroom Scanning Sensor
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

57. Earth Curvature Effect Whiskbroom Sensor
The effect is not significant for airborne systems and spaceborne earth observation remote sensing systems with relatively small swath widths.
Earth Curvature Effect
Whiskbroom Sensor
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

58. Whiskbroom Scanning Sensor Along-track Panoramic Distortion (Considering Earth Curvature)
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

59. Pushbroom Scanning Sensor Along-track Panoramic Distortion (Considering Earth Curvature)
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

60. Panoramic Distortion of Whiskbroom Sensor (Curved Surface)
Cross track
Along track
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

61. Panoramic Distortion of Pushbroom Sensor (Curved Surface)
Cross track
Along track
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

62. THREE COMPONENTS TO WARPING
Appropriate mathematical distortion model(s)
Orbit model
Platform attitude model
Scanner model
Earth model
Coordinate transformation
Resampling (interpolation)
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

63. Coordinate transformation
Mathematical Modeling for Geometric Corrections
Aspect-ratio distortion (oversampling)
Earth rotation
Rotation to north (orbit inclination angle)
Panoramic distortion
Combined correction
Polynomial Distortion Models
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

64. Correction for oversampling in cross-track direction (Aspect ratio correction)
Let (u0, v0) and (u, v) represent original and corrected image coordinates corresponding to a pixel. Define the oversampling rate as k1 = (Cross-track GSI/Along-track GSI) = Aspect Ratio. For example, Landsat MSS data has an H/V aspect ratio of 56/79 =
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

65. Correction for oversampling in the cross-track direction
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

66. Correction for Earth Rotation
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

67. Correction for Image Orientation to North-South (due to inclination angle)
where  = i – 90 and i is the orbit inclination angle.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

68. Correction for Panoramic Effects
The cross-track displacement for whiskbroom scanning sensor
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

69. Combined correction 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

70. Transforming Image Coordinates to Map Coordinates
If all distortions are corrected, the corrected image coordinates (u, v) and their corresponding map coordinates (x, y) are linearly related, i.e.,
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

71. (an affine transformation)
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

72. The above matrix equation is used for resampling.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

73. Polynomial Distortion Models
where N is the order of the polynomial.
N = 1  a linear polynomial (an affine transformation)
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

74. N = 2  a quadratic polynomial model
The coefficients in the polynomial can be associated with particular types of distortion.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

75. The coefficients in the polynomial can be associated with particular types of distortion
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

76. Different Effects of Distortion
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

77. Different Effects of Distortion
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

78. Different Effects of Distortion
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

79. The affine transformation can take into account the distortion effects of shift, scale, shear and rotation.
If an image has been processed accurately for systematic distortions, a linear polynomial may suffice for further correction.
A quadratic polynomial is sufficient for most problems in satellite remote sensing where the terrain relief is small and the FOV is not large.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

80. Determining the Polynomial Coefficients Using GCPs
A set of Ground Control Points (GCPs) can be chosen to solve for the coefficients in the polynomial.
GCPs should have the following characteristics:
high contrast in all images of interest
small feature size
unchanging over time
all are at the same elevation (unless topographic relief is being specifically addressed)
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

81. Examples of GCPs include road intersections, corners of agricultural fields, small islands and river features.
It is also desirable to find GCPs that are well-distributed over the image area.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

82. Each pair of GCP corresponds to two pairs of coordinates: (u0, v0) and (x, y).
Using M pairs of GCPs, we can set up a system of simultaneous equations and solve for polynomial coefficients.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

83. Similarly,
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

84. K : Number of polynomial coefficients N : Order of the polynomial
If M = K, then
We have an exact solution which passes through all GCPs, i.e., no mapping errors.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

85. It is usually desirable to have more GCPs, i.e. M > K .
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

86. Piecewise Polynomial Distortion Model
For severely-distorted images that can’t be modeled with a single, global polynomial of reasonable order.
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

87. THREE COMPONENTS TO WARPING
Appropriate mathematical distortion model(s)
Orbit model
Platform attitude model
Scanner model
Earth model
Coordinate transformation
Resampling (interpolation)
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

88. Implementation of Resampling
Create an empty output image (which is in the reference coordinate system)
Step through the integer reference coordinates, one at a time, and calculate the coordinates in the distorted image (u0,v0)
Estimate the pixel value to insert in the output image at (x, y) from the original image at (u0,v0).
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

89. 2/8/2018
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90. 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

91. Resampling Methods
Pixels are resampled using a weighted average of the neighboring pixels
Nearest neighbor method
Bilinear interpolation
Cubic convolution method
2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

92. 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

93. Bilinear interpolation
Nearest neighbor
Bilinear interpolation
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

94. Weight Functions
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

95. Cubic Convolution Parametric cubic convolution function
where ∆ is the distance from (x,y) to the grid points in 1-D.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

96. 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

97. 2/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

98. Resample along each row, A-D, E-H, I-L, M-P
Resample along new column Q-T
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.