Corrected the oblique resolution formula in the Camera class. Fixes #4614 (d4a9aced) · Commits · aflab / astrogeology / ISIS3

isis/src/base/objs/Camera/Camera.cpp

+16 −74

Original line number	Diff line number	Diff line
		@@ -568,74 +568,28 @@ namespace Isis {


		/**
		* @description This function provides an improved estimate of the detector resolution (in meters)
		* when the target is near the limb. It does this by calculating the determinant of an affine
		* transformation. The area element of one pixel projected onto the surface at Nadir looks
		* like a square with sides of length = Detector Resolution. The detector resolution is the
		* value returned by the original function. An affine projective transformation of this
		* area element as one would see if it was on the limb instead of looking straight down, appears
		* like a skewed parallelogram.
		* @description This method returns the Oblique Detector Resolution
		* if the Look Vector intersects the target and if the emission angle is greater than or equal
		* to 0, and less than 90 degrees. Otherwise, it returns -1.0. This formula provides an
		* improved estimate to the detector resolution for images near the limb:
		*
		* The determinant of the transformation matrix taking the Nadir-area element into
		* some parallelogram near the limb of a planet measures the change in area for the
		* transformation when we are off-Nadir. The sqare-root of the area of this parallelogram
		* gives us the resolution.
		*
		*The calculation is straightforward. Any affine transformation with a strictly positive
		*determinant that is not a similarity transformation has a unique decomposition
		*(See Theorem 2.1 in Reference #1):
		* @f[ \text{Oblique\;\;Detector\;\; Resolution} = \frac{n}{cos(\theta)} @f]
		*
		*
		* The equation is derived two separate ways. A geometric argument is presented in
		* Reference 2, while a matrix algebra based argument is presented in Theorem 2.1 of
		* Reference 1.
		*
		*
		* @f{eqnarray*}
		*
		* A = \[\left[\begin{array}{cc} a & b \\
		* c & d \end{array} \right]\] =
		*
		* H_{\lambda}R_1(\psi)T_tR_2(\phi) = \lambda
		* \[ \left[\begin{array}{cc} cos(\psi) & -sin(\psi) \\
		* sin(\psi) & cos(\psi) \end{array} \right]\]
		* \[ \left[\begin{array}{cc} t & 0 \\
		* 0 & 1 \end{array} \right]\]
		* \[ \left[\begin{array}{cc} cos(\phi) & -sin(\phi) \\
		* sin(\phi) & cos(\phi) \end{array} \right]\]
		*
		* @f}
		*
		* Where:
		*
		* @f$ t = \frac{1}{cos(\theta)}},\;\;\theta = \text{Emmission\;\; Angle}@f$
		* and @f$\lambda = \text{zoom\;\;factor} = 1@f$
		*
		* The determinant of A is:
		*
		* @f[ \|A\| = \lambda t = \frac{\lambda}{cos(\theta)} = \frac{1}{\cos(\theta)} @f]
		*
		* This is because the two rotation matrices in this decomposition have determinants equal to 1.
		*
		* Let @f$ n = \text{Detector\;\;Resolution} @f$
		*
		* Then:
		*
		* @f[ Area = n^2 \|A\| =\frac{n^2}{cos(\theta)}@f]
		*
		* And:
		*
		* @f[ \text{Local\;\;Detector\;\; Resolution} = \frac{n}{\sqrt{cos(\theta)}} @f]
		*
		*
		* This method returns the Local Detector Resolution if the Look Vector intersects the target
		* and if @f$ 0 \leq \theta < \frac{\pi}{2} @f$ and -1.0 otherwise.
		*
		*
		*
		*
		* Reference 1: J-M Morel and G. Yu, "Asift: A new framework for fully affine
		* <b>Reference 1:</b> J-M Morel and G. Yu, "Asift: A new framework for fully affine
		* invariant image comparison," SIAM Journal on Imaging Sciences
		* 2(2), pp. 438-469, 2009
		*
		*
		* <b>Reference 2:</b> Handwritten notes by Orrin Thomas which can be found in the
		* Glossary under the entry for Oblique Detector Resolution.
		*
		* @return @b double
		*/
		double Camera::ObliqueDetectorResolution(){
		@@ -643,23 +597,11 @@ namespace Isis {

		if(HasSurfaceIntersection()){


		double thetaRad;
		double sB[3];
		instrumentPosition(sB);
		double pB[3];
		Coordinate(pB);
		double a = sB[0] - pB[0];
		double b = sB[1] - pB[1];
		double c = sB[2] - pB[2];
		double rho = sqrt(a * a + b * b + c * c) * 1000.0;

		thetaRad = EmissionAngle()*DEG2RAD;

		if (thetaRad < HALFPI) {

		double nadirResolution = rho/(p_focalLength/p_pixelPitch);
		return nadirResolution/sqrt(cos(thetaRad));
		return DetectorResolution()/cos(thetaRad);

		}
		return Isis::Null;

isis/src/base/objs/Camera/Camera.truth

+4 −4

Original line number	Diff line number	Diff line
		@@ -84,13 +84,13 @@ GroundRange: 0
		IntersectsLongitudeDomain: 0
		PixelResolution: 628
		ExposureDuration: 0.4
		ObliquePixelResolution: 685
		ObliquePixelResolution: 748
		LineResolution: 628
		ObliqueLineResolution: 685
		ObliqueLineResolution: 748
		SampleResolution: 628
		ObliqueSampleResolution: 685
		ObliqueSampleResolution: 748
		DetectorResolution: 157
		ObliqueDetectorResolution: 171
		ObliqueDetectorResolution: 187
		LowestImageResolution: 2047
		HighestImageResolution: 430
		Calling BasicMapping (pvl)...

isis/src/base/objs/CameraPointInfo/CameraPointInfo.truth

+8 −8

Original line number	Diff line number	Diff line
		@@ -15,10 +15,10 @@ Group = GroundPoint
		LocalRadius = 1737400.0 <meters>
		SampleResolution = 187.48511798825 <meters/pixel>
		LineResolution = 187.48511798825 <meters/pixel>
		ObliqueDetectorResolution = 187.48933248321 <meters>
		ObliquePixelResolution = 187.48933248321 <meters/pix>
		ObliqueLineResolution = 187.48933248321 <meters>
		ObliqueSampleResolution = 187.48933248321 <meters>
		ObliqueDetectorResolution = 187.49354707291 <meters>
		ObliquePixelResolution = 187.49354707291 <meters/pix>
		ObliqueLineResolution = 187.49354707291 <meters>
		ObliqueSampleResolution = 187.49354707291 <meters>

		# Spacecraft Information
		SpacecraftPosition = (216.76438021037, 54.256829538645,
		@@ -77,10 +77,10 @@ Group = GroundPoint
		LocalRadius = 1737400.0 <meters>
		SampleResolution = 187.50339379912 <meters/pixel>
		LineResolution = 187.50339379912 <meters/pixel>
		ObliqueDetectorResolution = 187.52061363579 <meters>
		ObliquePixelResolution = 187.52061363579 <meters/pix>
		ObliqueLineResolution = 187.52061363579 <meters>
		ObliqueSampleResolution = 187.52061363579 <meters>
		ObliqueDetectorResolution = 187.53783505388 <meters>
		ObliquePixelResolution = 187.53783505388 <meters/pix>
		ObliqueLineResolution = 187.53783505388 <meters>
		ObliqueSampleResolution = 187.53783505388 <meters>

		# Spacecraft Information
		SpacecraftPosition = (216.76438021037, 54.256829538645,

isis/src/base/objs/CameraStatistics/CameraStatistics.truth

+9 −9

Original line number	Diff line number	Diff line
		@@ -38,21 +38,21 @@ Resolution:

		ObliqueSampleResolution:
		ObliqueSampleResolutionMinimum = 244.735
		ObliqueSampleResolutionMaximum = 246.319
		ObliqueSampleResolutionAverage = 245.205
		ObliqueSampleResolutionStandardDeviation = 0.304432
		ObliqueSampleResolutionMaximum = 246.963
		ObliqueSampleResolutionAverage = 245.396
		ObliqueSampleResolutionStandardDeviation = 0.428052

		ObliqueLineResolution:
		ObliqueLineResolutionMinimum = 244.735
		ObliqueLineResolutionMaximum = 246.319
		ObliqueLineResolutionAverage = 245.205
		ObliqueLineResolutionStandardDeviation = 0.304432
		ObliqueLineResolutionMaximum = 246.963
		ObliqueLineResolutionAverage = 245.396
		ObliqueLineResolutionStandardDeviation = 0.428052

		ObliqueResolution:
		ObliqueResolutionMinimum = 244.735
		ObliqueResolutionMaximum = 246.319
		ObliqueResolutionAverage = 245.205
		ObliqueResolutionStandardDeviation = 0.304432
		ObliqueResolutionMaximum = 246.963
		ObliqueResolutionAverage = 245.396
		ObliqueResolutionStandardDeviation = 0.428052

		AspectRatio:
		AspectRatioMinimum = 1

isis/src/docsys/documents/Glossary/Glossary.xml

+15 −8

Original line number	Diff line number	Diff line
		@@ -397,16 +397,18 @@

		<definition name="Oblique Detector Resolution"><a name="oblique_detector_resolution"></a>
		This provides an improved estimate to the standard <a href="#detector_resolution">detector resolution</a> when the image is taken at an oblique
		angle. It returns the square-root of the area of the projection of the detector onto the body of the target (in units of meters).
		If the image is taken at nadir, this is the ground distance between the left and right edge of the detector, because the
		detector's projection is a square. For off-nadir images, the projection has a trapezoidal shape.
		In Figure 1A below, an image of the Dufay X crater that was taken near nadir is displayed. Figure 1B is a
		angle. In Figure 1A below, an image of the Dufay X crater that was taken near nadir is displayed. Figure 1B is a
		color map showing the relative difference between the oblique detector resolution, and the original detector resolution as a function
		of the emission angle. For small emission angles (near nadir) the relative difference between the two estimates
		is very small. For larger emission angles (off-nadir), the relative difference between the
		two estimates increases rapidly. Figure 2A is an image of the Carlini crater group taken at an oblique angle. Figure 2B is a color plot
		of the relative difference between the two estimates showing a minimum value of approximately 50% between the two when the
		emission angles off-nadir are in the range 65-75 degrees.
		of the relative difference between the two estimates showing a minimum of approximately 120% when the
		emission angles off-nadir are in the range 64-75 degrees. The traditional approximation is obviously not adequate for a case such
		as this, and the oblique detector resolution should be used.






		<table border = "1">
		@@ -433,7 +435,7 @@
		<tr>
		<td>
		<center>
		<image width="584" height="492" src="assets/nadir40pct.png">
		<image width="585" height="487" src="assets/nadir_scaled.png">
		<brief><br><strong>Fig 1B:</strong> Relative percentage difference between resolution estimates for</br>
		<br> a nadir image (see <strong>Fig. 1A</strong>).</br></brief>
		</image>
		@@ -441,7 +443,7 @@
		</td>
		<td>
		<center>
		<image width="582" height="492" src="assets/oblique40pct.png">
		<image width="583" height="487" src="assets/oblique_scaled.png">
		<brief><br><strong>Fig 2B:</strong> Relative percentage difference between resolution estimates for</br>
		<br> an oblique image (see <strong>Fig. 2A</strong>).</br></brief>
		</image>
		@@ -449,6 +451,11 @@
		</td>
		</tr>
		</table>


		Handwritten notes by Orrin Thomas giving a geometric justification for this method can be found <a href="assets/oblique.pdf">here.</a>


		</definition>

		<definition name="I/F">