Recent changes to AlgorithmDescription

AlgorithmDescription modified by Rupesh Shrestha

Rupesh Shrestha — Wed, 04 Dec 2013 17:25:55 -0000

--- v4
+++ v5
@@ -1,13 +1,13 @@
 MCC Algorithm
 ============
-SD : scale domain, integer in \[1,3\] (variable *l (lowercase "L")* in paper)
+SD : scale domain, integer in \[1,3\] (variable *l (lowercase "L")* in [paper](http://www.treesearch.fs.fed.us/pubs/29032))

 t_SD: curvature tolerance for scale domain SD
 t₁ = *specified by user*
 t₂ = t₁ + 0.1
 t₃ = t₂ + 0.1

-CR_SD : cell resolution for scale domain SD (lambda variable in paper)
+CR_SD : cell resolution for scale domain SD (lambda variable in [paper](http://www.treesearch.fs.fed.us/pubs/29032))
 CR₁ = 0.5 * CR₂
 CR₂ = *specified by user (nominal post-spacing of input LiDAR data)*
 CR₃ = 1.5 * CR₂

AlgorithmDescription modified by Rupesh Shrestha

Rupesh Shrestha — Wed, 04 Dec 2013 16:48:56 -0000

--- v3
+++ v4
@@ -22,7 +22,7 @@
 P_j = (x_j , y_j , z_j)
 U₀ = *initial point-cloud data specified by user*

-  1.  U = [filter out higher points at same x,y](#PointsAtSameXY) in U₀ and classify them as non-ground
+  1.  U = [filter out higher points at same x,y](AlgorithmFilterXY) in U₀ and classify them as non-ground
   1.  for scale domain (SD) = 1 to 3:
   1.  . . repeat
   1.  . . . . S = interpolate new raster surface using TPS(U, CR_SD, f)
@@ -33,14 +33,3 @@
   1.  . . . . n_C : # of points classified and removed from U during current iteration through inner loop
   1.  . . until n_C < 0.1% * n
   1.  classify all the points remaining in U as ground
-
-
-Filtering Out Points at Same X,Y #PointsAtSameXY
--------
-Interpolation of a raster surface requires that no two points have the same x and y coordinates (it causes problems mathematically).  If two or more points are at the same x,y location, then all the points except the lowest point (i.e., with minimum z coordinate) must be non-ground.  So those higher points can be classified and removed from the list of unclassified points.
-
-  1.  for each x,y location in U₀ with two or points:
-  1.  . . z_lowest = minimum z coordinate of the points at x,y
-  1.  . . for each point P_j at x,y:
-  1.  . . . . if z_j > z_lowest then
-  1.  . . . . . . classify P_j as non-ground and remove it from U₀

AlgorithmDescription modified by Rupesh Shrestha

Rupesh Shrestha — Wed, 04 Dec 2013 16:37:55 -0000

--- v2
+++ v3
@@ -1,52 +1,46 @@
 MCC Algorithm
 ============
+SD : scale domain, integer in \[1,3\] (variable *l (lowercase "L")* in paper)

-SD : scale domain, integer in [1,3] (variable ''l (lowercase "L")'' in paper)
+t_SD: curvature tolerance for scale domain SD
+t₁ = *specified by user*
+t₂ = t₁ + 0.1
+t₃ = t₂ + 0.1

-t,,SD,, : curvature tolerance for scale domain SD  [[br]]
-t,,1,, = ''specified by user''                     [[br]]
-t,,2,, = t,,1,, + 0.1                              [[br]]
-t,,3,, = t,,2,, + 0.1
+CR_SD : cell resolution for scale domain SD (lambda variable in paper)
+CR₁ = 0.5 * CR₂
+CR₂ = *specified by user (nominal post-spacing of input LiDAR data)*
+CR₃ = 1.5 * CR₂

-CR,,SD,, : cell resolution for scale domain SD (lambda variable in paper)  [[br]]
-CR,,1,, = 0.5 * CR,,2,,                                                    [[br]]
-CR,,2,, = ''specified by user (nominal post-spacing of input LiDAR data)'' [[br]]
-CR,,3,, = 1.5 * CR,,2,,
-
-f : tension parameter (invariant across scale domains)  [[br]]
+f : tension parameter (invariant across scale domains)
 f = 1.5

-U : vector of points that remain unclassified           [[br]]
-U = (P,,1,, , P,,2,, , P,,3,, , ... P,,n,,)             [[br]]
-n : # of points in U (at the start of each loop pass)   [[br]]
-P,,j,, : single LiDAR point                             [[br]]
-P,,j,, = (x,,j,, , y,,j,, , z,,j,,)                     [[br]]
-U,,0,, = ''initial point-cloud data specified by user''
+U : vector of points that remain unclassified
+U = (P₁ , P₂ , P₃ , ... P_n)
+n : # of points in U (at the start of each loop pass)
+P_j : single LiDAR point
+P_j = (x_j , y_j , z_j)
+U₀ = *initial point-cloud data specified by user*

-  1.  U = [#PointsAtSameXY filter out higher points at same x,y] in U,,0,, and classify them as non-ground
+  1.  U = [filter out higher points at same x,y](#PointsAtSameXY) in U₀ and classify them as non-ground
   1.  for scale domain (SD) = 1 to 3:
   1.  . . repeat
-  1.  . . . . S = interpolate new raster surface using TPS(U, CR,,SD,,, f)
+  1.  . . . . S = interpolate new raster surface using TPS(U, CR_SD, f)
   1.  . . . . S' = surface resulting from passing 3x3 averaging kernel over S
-  1.  . . . . for each point P,,j,, in U:
-  1.  . . . . . . if z,,j,, > S'(x,,j,, , y,,j,,) + t,,SD,, then
-  1.  . . . . . . . . classify P,,j,, as non-ground and remove it from U
-  1.  . . . . n,,C,, : # of points classified and removed from U during current iteration through inner loop
-  1.  . . until n,,C,, < 0.1% * n
+  1.  . . . . for each point P_j in U:
+  1.  . . . . . . if z_j > S'(x_j , y_j) + t_SD then
+  1.  . . . . . . . . classify P_j as non-ground and remove it from U
+  1.  . . . . n_C : # of points classified and removed from U during current iteration through inner loop
+  1.  . . until n_C < 0.1% * n
   1.  classify all the points remaining in U as ground

 Filtering Out Points at Same X,Y #PointsAtSameXY
 -------
+Interpolation of a raster surface requires that no two points have the same x and y coordinates (it causes problems mathematically).  If two or more points are at the same x,y location, then all the points except the lowest point (i.e., with minimum z coordinate) must be non-ground.  So those higher points can be classified and removed from the list of unclassified points.

-Interpolation of a raster surface requires that no two points have the same
-x and y coordinates (it causes problems mathematically).  If two or more
-points are at the same x,y location, then all the points except the lowest
-point (i.e., with minimum z coordinate) must be non-ground.  So those higher
-points can be classified and removed from the list of unclassified points.
-
-    1.  for each x,y location in U,,0,, with two or points:
-    1.  . . z,,lowest,, = minimum z coordinate of the points at x,y
-    1.  . . for each point P,,j,, at x,y:
-    1.  . . . . if z,,j,, > z,,lowest,, then
-    1.  . . . . . . classify P,,j,, as non-ground and remove it from U,,0,,
+  1.  for each x,y location in U₀ with two or points:
+  1.  . . z_lowest = minimum z coordinate of the points at x,y
+  1.  . . for each point P_j at x,y:
+  1.  . . . . if z_j > z_lowest then
+  1.  . . . . . . classify P_j as non-ground and remove it from U₀

AlgorithmDescription modified by Rupesh Shrestha

Rupesh Shrestha — Wed, 04 Dec 2013 15:29:19 -0000

--- v1
+++ v2
@@ -1,7 +1,7 @@
 MCC Algorithm
 ============

-SD : scale domain, integer in ![1,3] (variable ''l (lowercase "L")'' in paper)
+SD : scale domain, integer in [1,3] (variable ''l (lowercase "L")'' in paper)

 t,,SD,, : curvature tolerance for scale domain SD  [[br]]
 t,,1,, = ''specified by user''                     [[br]]

AlgorithmDescription modified by Rupesh Shrestha

Rupesh Shrestha — Wed, 04 Dec 2013 15:28:27 -0000

MCC Algorithm

SD : scale domain, integer in '' in paper)

t,,SD,, : curvature tolerance for scale domain SD [[br]]
t,,1,, = ''specified by user'' [[br]]
t,,2,, = t,,1,, + 0.1 [[br]]
t,,3,, = t,,2,, + 0.1

CR,,SD,, : cell resolution for scale domain SD (lambda variable in paper) [[br]]
CR,,1,, = 0.5 * CR,,2,, [[br]]
CR,,2,, = ''specified by user (nominal post-spacing of input LiDAR data)'' [[br]]
CR,,3,, = 1.5 * CR,,2,,

f : tension parameter (invariant across scale domains) [[br]]
f = 1.5

U : vector of points that remain unclassified [[br]]
U = (P,,1,, , P,,2,, , P,,3,, , ... P,,n,,) [[br]]
n : # of points in U (at the start of each loop pass) [[br]]
P,,j,, : single LiDAR point [[br]]
P,,j,, = (x,,j,, , y,,j,, , z,,j,,) [[br]]
U,,0,, = ''initial point-cloud data specified by user''

U = [#PointsAtSameXY filter out higher points at same x,y] in U,,0,, and classify them as non-ground
for scale domain (SD) = 1 to 3:
. . repeat
. . . . S = interpolate new raster surface using TPS(U, CR,,SD,,, f)
. . . . S' = surface resulting from passing 3x3 averaging kernel over S
. . . . for each point P,,j,, in U:
. . . . . . if z,,j,, > S'(x,,j,, , y,,j,,) + t,,SD,, then
. . . . . . . . classify P,,j,, as non-ground and remove it from U
. . . . n,,C,, : # of points classified and removed from U during current iteration through inner loop
. . until n,,C,, < 0.1% * n
classify all the points remaining in U as ground

Filtering Out Points at Same X,Y #PointsAtSameXY

Interpolation of a raster surface requires that no two points have the same
x and y coordinates (it causes problems mathematically). If two or more
points are at the same x,y location, then all the points except the lowest
point (i.e., with minimum z coordinate) must be non-ground. So those higher
points can be classified and removed from the list of unclassified points.

1.  for each x,y location in U,,0,, with two or points:
1.  . . z,,lowest,, = minimum z coordinate of the points at x,y
1.  . . for each point P,,j,, at x,y:
1.  . . . . if z,,j,, > z,,lowest,, then
1.  . . . . . . classify P,,j,, as non-ground and remove it from U,,0,,