Changeset 41924 for branches/eam_branches/ipp-20211108

Timestamp:

Nov 22, 2021, 9:45:09 AM (5 years ago)

Author:

eugene

Message:

tweak to the variance: should use nGood pixels in demoninator

File:

• branches/eam_branches/ipp-20211108/psModules/src/imcombine/pmStack.c (modified) (2 diffs)

branches/eam_branches/ipp-20211108/psModules/src/imcombine/pmStack.c

@@ -400 +400 @@
     //     variance_combination = variance_individual / N
     // which makes sense --- the standard deviation of the combination is reduced by a factor of sqrt(N).
+    // NOTE: in 2012.07.13, the variance calculation was changed without justification to the variance
+    // appropriate to a weighted mean, while the pixel mean was kept as the average unweighted by pixel variance
 
     float sumValueWeight = 0.0;         // Sum of the value multiplied by the weight
@@ -1686 +1688 @@
             // }
             // variance on the mean (stdev / sqrt(N))^2
-            float varValue = varSum / (Npt*Npt);
+
+            // Note: since we are calculating the average of a subset of a sorted
+            // list of values, the denominator should not be the number of measurements
+            // in the calculation above (Npt): in the extreme case of a median, we would
+            // have a single value (Npt = 1), but the variance of a median is only ~1.4 x
+            // the variance of the average / sqrt(N).  We should use nGood (the total number
+            // of values in the sorted list), but the variance should be scaled by a factor
+            // which depends on the fraction of values included.  
+
+            // this coefficient varies between 1.4 (for pure median) and 1.05 for 68% range.
+
+            float varValue = varSum / (float) (nGood*nGood);
 
             combined->image->data.F32[y][x] = mean;