GEOMETRIC CORRECTION OF REMOTELY SENSED IMAGERY
Systematic Errors: Corrected through analysis of system characteristics and ephemeris Scan Skew: Caused by the forward motion if the platform during the time required for each mirror sweep. The ground swath is not normal t o the ground track but is slightly skewed, producing crosscross -scan geometric distortion MirrorMirror-Scan Velocity Variance: The mirror scanning rate is usually not constant across a given scan, producing along -scan geometric distortion. he tangent Panoramic Distortion: The ground area imaged is proportional to tthe of the scan angle rather than to the angle itself. Because data are sampled at regular intervals, this produces alongalong-scan distortion Platform Velocity: If the speed of the the platform changes, the ground track covered by successive mirror scans changes, producing along -track scale distortion Earth Rotation: Earth rotates as the sensor scans the terrain. This results in a shift of the ground swath being scanned, causing alongalong -scan distortion. Types ofErrors
Non Non- Systematic Errors:
Corrected through the use of ground control points ( GCP ( GCP ’ ’s )
Altitude Variance: If the sensor platform departs from its normal altitude or the terrain increases in elevation, this produces changes in scale or pixel size Platform Attitude: One sensor system axis is usually maintained normal to Earth's surface and the other parallel to the spacecraft's direction of travel. If the sensor departs form this attitude, geometric distortion results.
Definitions Ephemeris: Any tabular statement of the the assigned assigned places placesof of a celestial body for regular regular intervals (Websters (Websters Dict.). Dict.). For example, example, the solar solar ephemeris ephemeris provides provides the exact exact location location of the sun at any given given time of the the day or year. Geocoding: Geocoding: Geographical referencing or coding of data. (Jensen, 1986) Ground Control Point (GCP): A specific pixel on an image or location on a map whose geographic coordinates are known. GCP's are used to to correct geometric geometric distortion distortion in an image by matching image coordinates with map coordinates. Linear Transformation: The transformation of coordinates from one system to another (image (image to map) using a linear linear algebraic algebraic(1st (1storder orderpolynomial) polynomial)f f ormula ormula . NonNon-Linear Transformation: The transformation of coordinates from one system to another (image to map) using a non -linear algebraic (Nth order polynomial) formula Rectification: The process by which the geometry of an image is made planimetric. planimetric. (Jensen, (Jensen, 1986) Registration: Registration:The The process process of of geometrically geometricallyaligning aligningtwo aligning two or or more more sets of image data such that resolution cells for a single ground area can be digit ally visually ally or visually superimposed. A map coordinate system may not be involved.
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Definitions (cont.)
Orbital Characteristics
Resampling: Resampling: The process of extrapolating data values to a new grid. Resampling is the step in rectifying an image that calculates pixel values for the rectified rectified grid from the original original data grid. grid. Root Mean Square Error (RMS) : The RMS is the error term used to determine the accuracy of the transformation from one coordinate system to ano ther. It is the difference between the desired output coordinate for a GCP and the actual
RMS = SQRT ( (X ’ – Xorig )2 + (Y’ (Y’ – Yorig)2 )
Image to Ground Geocorrection: Geocorrection: The correction of digital images to ground coordinates using ground control points collected from maps or GPS.
Sun Synchronous orbits have a angle of inclination of 98.2 degrees from the equator. This results in a “ nonnon-vertical vertical ” ” north orientation. orientation. Further, the Earth rotates on it ’ ’s axis from west to east as the imagery is collected.
Image to Image Geocorrection: Geocorrection: Image to Image correction involves matching the coordinate systems of one digital image to another image acting as a map map reference. reference.
Imagery collected from sensors consist of a rectangular array of pixels which include the effects of earth rotation. Correction of scan lines to account for earth rotation rotation consists of systematically offsetting scans to the west.
Cross-Track Scan Errors This type of error is a function of the distance from the sensor to the target, the instantaneous field of view (IFOV), and the scan angle off nadir. This type of error is termed “ Tangential Tangential ” distortion ” distortion as compared to “ Radial ” ” distortion present in analog aerial photographs.
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Ground Control Points
Landsat 30m ETM+ Image
Ground Control Points
Quickbird Quickbird .7m .7m Natural Color Image
The Landsat 30m ETM+ image represents the unrectified dataset. unrectified dataset. The Quickbird .7m .7m image is being used as the geographic reference. The two images vary in spatial resolution. The reference image should be be at least as resolute as the unrectified image. unrectified image.
Root Mean Square Error
Landsat 30m ETM+ Image
Quickbird .7m .7m Natural Color Image
Ground control points are identified between the two images in r ecognizable ecognizable locations. These points should be static relative relative to to temporal temporal change. change. In this case road intersections are the best source of GCP ’ ’s . Features that move through time (i.e. shorelines, etc.) should be avoided if possible. possible.
Calculation of Total RMS
Using a minimum of 4 GCP’ GCP’s, the RMS error is computed as the distance between the input (source) location of a GCP and the retransformed location for the same GCP.
e t a n i d r o o c X e c n e r e f e R
X Residual
l a u d i s e R Y
Source X Coordinate
RMS error is calculated when enough GCP points are collected to define the relationship between the source coordinate system and the reference.
Ri =
RMS error
2
2
XRi + YRi
Ri = RMS for GCP i XR = X residual for GCP i YR = Y residual for GCP i
Where: R x = X RMS error R y= Y RMS error T = total RMS error n= the number of GCPs
i = GCP number XRi = the X residual for GCP i YRi = the Y residual for GCP i
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Point Contribution to Total RMS
Evaluating RMS Error Aft er each com put atio n of a tran sfo rmat ion and RMS err or, t here are four options:
Where: E i = error contribution of GCPi Ri = the RMS error for GCPi T = total RMS error
This value reports the normalized contribution contribution of of individual GCP’ GCP’s to the total RMS
• Throw out the GCP with tthe he highest RMS error, assuming that thi s GCP is the least accurate. This assumption should be tested by reviewing the location of the point on the image relative to the reference. Do not take the high RMS for a point for granted. Also, Also, if this is tthhe specific region of the image, removing e only point in aa specific n g the point may be problematic • Tolerate a higher amount re-amount of RMS error. error. If point point removal removal or re allignment cannot be justified. • Increase increasing Increase the the complexity complexity of of transformation by in creasing the the order order of the polynomial. This is justified with imagery that is known to to have non -linear distortion. Using a higher higher polynomial may also also “ over -fit ” the estimate. • Select Select only only the the points points for which you you have the most confidence.
Nearest Neighbor The nearest neighbor approach uses the value of the closest inpu t pixel for the ouput pixel value. To determine determine the the nearest neighbor, the algorithm u ses the inverse of the transformation matrix to calculate the image file coordinates of the desired geographic coordinate. The pixel value occupying the clo sest image file coordinate to the estimated coordinate will be used for the outp ut pixel value in the georeferenced image.
Nearest Neighbor (cont.) ADVANTAGES:
• Output values are the original input values. Other methods of resampling tend to average surrounding values. This may be an important consideration when discriminating between vegetation types or lo cating boundaries. • Since original data are retained, this method is recommended bef ore bef ore classification. • Easy to compute and therefore fastest to use . DISADVANTAGES:
• Produces a choppy, "stair"stair-stepped" effect. The image has a rough appearance relative to the original unrectified data. • Data values may be lost, while other values may be duplicated. F igure 1 shows an input file (orange) with a yellow output file superimpo sed. Input values closest to the center of each output cell are sent to the output file to the right. Notice that values 13 and 22 are lost while values 14 and 24 are duplicated.
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Nearest Neighbor (cont.) Unrectified raster image
Nearest Neighbor (cont.)
Brightness value matrix of unrectified image
The concept of the Nearest Nearest Neighbor Neighbor is is to geographically locate the nearest pixel in the input file to the output file pixel location. location.
Rectified using nearest neighbor resamp. BV matrix of nearest neighbor resampled image
Bilinear Interpolation
Bilinear Interpolation (cont.)
The bilinear interpolation approach uses the weighted average of the nearest four pixels to the output pixel. 4
Z k
Σ D2 k
K = 1
BV wt =
4
1
Σ D2 k
Where: Z = Surrounding 4 data points D = Distance to each point
ADVANTAGES: • StairStair-step effect caused by the nearest neighbor approach is reduced. Image looks smooth.
K = 1
DISADVANTAGES: • Alters original data and reduces contrast by averaging neighboring values together. • Is computationally more expensive than nearest neighbor.
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Bilinear Interpolation (cont.) Unrectified raster image
Brightness value matrix of unrectified image
Cubic Convolution The cubic convolution approach uses the weighted average of the nearest sixteen pixels to the output pixel. The output is similar to bilinear interpolation, but the smoothing effect caused by the a veraging of surrounding input pixel values is more dramatic. 16
Z k
Σ 2 K = 1 D k Rectified using bilinear interpolation resampling. Notice the dark edge cells created by averaging zero values located around the perimeter of the ouput file into real data values BV matrix of nearest neighbor resampled image
Cubic Convolution (cont.)
BV wt =
16
1
Where: Z = Surrounding 4 data points D = Distance to each point
Σ D2 k
K = 1
Cubic Convolution (cont.) Unrectified raster image
Brightness value matrix of unrectified image
ADVANTAGES:
• Stair-step effect caused by the nearest neighbor approach is reduced. Image looks smooth.
DISADVANTAGES:
• Alters original data and reduces contrast by averaging neighboring values together.
Rectified using cubic convolution resampling. Notice the dark edge cells created by averaging zero values located around the perimeter of the ouput file into real data values
BV matrix of cubic convol. resampled image
• Is computationally more expensive than nearest neighbor or bilinear interpolation.
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Nearest Neighbor subtracted from Bilinear Interpolation
Nearest Neighbor subtracted from Cubic Convolution
band min max mean stdv
band min max mean stdv
1
0
98
2.2
3.2
1
0
116
2.6
3.6
2
0
92
1.2
2.0
2
0
105
1.5
2.3
3.0
3
0
133
2.6
3.5
0
66
3.4
3.9
3
0
113
2.2
4
0
65
2.8
3.3
4
5
0
69
3.5
4.0
5
0
90
4.2
4.7
0.6
6
0
9
0.6
0.7
2.7
7
0
73
2.7
3.1
6 7
0 0
8 76
0.4 2.3
Bilinear Interpolation subtracted from Cubic Convolution NN - BL
NN - CC
BL - CC
band min max mean stdv
min max mean stdv
min max mean stdv
1
0
3.6
0
52
1.3
1.8
51
0.8
1.2
0
98
2.2
3.2
116
2.6
2
0
92
1.2
2.0
0
105
1.5
2.3
0
band min max mean stdv
3
0
113
2.2
3.0
0
133
2.6
3.5
0
46
1.4
1.7
1
0
52
1.3
1.8
4
0
65
2.8
3.3
0
66
3.4
3.9
0
35
1.7
1.9
2
0
51
0.8
1.2
5
0
69
3.5
4.0
0
90
4.2
4.7
0
41
2.2
2.3
3
0
46
1.4
1.7
6
0
8
0.4
0.6
0
9
0.6
0.7
0
3
0.2
0.4
4
0
35
1.7
1.9
7
0
76
2.3
2.7
0
73
2.7
3.1
0
46
1.4
1.5
5
0
41
2.2
2.3
6
0
3
0.2
0.4
7
0
46
1.4
1.5
7
