1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
|
From: various upstream authors authors
Description: Implement bicubic interpolation correctly
This patch fixes a bug triggered by octave-image's test suite.
Origin: upstream, http://hg.savannah.gnu.org/hgweb/octave/file/62bb59f927b1/scripts/general/interp2.m
Bug-Debian: http://bugs.debian.org/582276
--- a/scripts/general/interp2.m
+++ b/scripts/general/interp2.m
@@ -57,7 +57,7 @@
## @item 'linear'
## Linear interpolation from nearest neighbors.
## @item 'pchip'
-## Piece-wise cubic hermite interpolating polynomial (not implemented yet).
+## Piece-wise cubic hermite interpolating polynomial.
## @item 'cubic'
## Cubic interpolation from four nearest neighbors.
## @item 'spline'
@@ -218,18 +218,21 @@
c = Z(2:zr, 1:(zc - 1)) - a;
d = Z(2:zr, 2:zc) - a - b - c;
- idx = sub2ind (size (a), yidx, xidx);
-
## scale XI, YI values to a 1-spaced grid
- Xsc = (XI - X(xidx)) ./ (X(xidx + 1) - X(xidx));
- Ysc = (YI - Y(yidx)) ./ (Y(yidx + 1) - Y(yidx));
+ Xsc = (XI - X(xidx)) ./ (diff (X)(xidx));
+ Ysc = (YI - Y(yidx)) ./ (diff (Y)(yidx));
+
+ ## Get 2D index.
+ idx = sub2ind (size (a), yidx, xidx);
+ ## We can dispose of the 1D indices at this point to save memory.
+ clear xidx yidx
## apply plane equation
ZI = a(idx) + b(idx).*Xsc + c(idx).*Ysc + d(idx).*Xsc.*Ysc;
elseif (strcmp (method, "nearest"))
- ii = (XI - X(xidx) > X(xidx + 1) - XI);
- jj = (YI - Y(yidx) > Y(yidx + 1) - YI);
+ ii = (XI - X(xidx) >= X(xidx + 1) - XI);
+ jj = (YI - Y(yidx) >= Y(yidx + 1) - YI);
idx = sub2ind (size (Z), yidx+jj, xidx+ii);
ZI = Z(idx);
@@ -339,11 +342,64 @@
## FIXME bicubic/__splinen__ don't handle arbitrary XI, YI
if (strcmp (method, "cubic"))
- ZI = bicubic (X, Y, Z, XI(1,:), YI(:,1), extrapval);
+ if (isgriddata (XI) && isgriddata (YI'))
+ ZI = bicubic (X, Y, Z, XI (1, :), YI (:, 1), extrapval);
+ elseif (isgriddata (X) && isgriddata (Y'))
+ ## Allocate output
+ ZI = zeros (size (X));
+
+ ## Find inliers
+ inside = !(XI < X (1) | XI > X (end) | YI < Y (1) | YI > Y (end));
+
+ ## Scale XI and YI to match indices of Z
+ XI = (columns (Z) - 1) * (XI - X (1)) / (X (end) - X (1)) + 1;
+ YI = (rows (Z) - 1) * (YI - Y (1)) / (Y (end) - Y (1)) + 1;
+
+ ## Start the real work
+ K = floor (XI);
+ L = floor (YI);
+
+ ## Coefficients
+ AY1 = bc ((YI - L + 1));
+ AX1 = bc ((XI - K + 1));
+ AY0 = bc ((YI - L + 0));
+ AX0 = bc ((XI - K + 0));
+ AY_1 = bc ((YI - L - 1));
+ AX_1 = bc ((XI - K - 1));
+ AY_2 = bc ((YI - L - 2));
+ AX_2 = bc ((XI - K - 2));
+
+ ## Perform interpolation
+ sz = size(Z);
+ ZI = AY_2 .* AX_2 .* Z (sym_sub2ind (sz, L+2, K+2)) ...
+ + AY_2 .* AX_1 .* Z (sym_sub2ind (sz, L+2, K+1)) ...
+ + AY_2 .* AX0 .* Z (sym_sub2ind (sz, L+2, K)) ...
+ + AY_2 .* AX1 .* Z (sym_sub2ind (sz, L+2, K-1)) ...
+ + AY_1 .* AX_2 .* Z (sym_sub2ind (sz, L+1, K+2)) ...
+ + AY_1 .* AX_1 .* Z (sym_sub2ind (sz, L+1, K+1)) ...
+ + AY_1 .* AX0 .* Z (sym_sub2ind (sz, L+1, K)) ...
+ + AY_1 .* AX1 .* Z (sym_sub2ind (sz, L+1, K-1)) ...
+ + AY0 .* AX_2 .* Z (sym_sub2ind (sz, L, K+2)) ...
+ + AY0 .* AX_1 .* Z (sym_sub2ind (sz, L, K+1)) ...
+ + AY0 .* AX0 .* Z (sym_sub2ind (sz, L, K)) ...
+ + AY0 .* AX1 .* Z (sym_sub2ind (sz, L, K-1)) ...
+ + AY1 .* AX_2 .* Z (sym_sub2ind (sz, L-1, K+2)) ...
+ + AY1 .* AX_1 .* Z (sym_sub2ind (sz, L-1, K+1)) ...
+ + AY1 .* AX0 .* Z (sym_sub2ind (sz, L-1, K)) ...
+ + AY1 .* AX1 .* Z (sym_sub2ind (sz, L-1, K-1));
+ ZI (!inside) = extrapval;
+
+ else
+ error ("interp2: input data must have `meshgrid' format");
+ endif
elseif (strcmp (method, "spline"))
- ZI = __splinen__ ({Y(:,1).', X(1,:)}, Z, {YI(:,1), XI(1,:)}, extrapval,
+ if (isgriddata (XI) && isgriddata (YI'))
+ ZI = __splinen__ ({Y(:,1).', X(1,:)}, Z, {YI(:,1), XI(1,:)}, extrapval,
"spline");
+ else
+ error ("interp2: input data must have `meshgrid' format");
+ endif
else
error ("interpolation method not recognized");
endif
@@ -351,6 +407,38 @@
endif
endfunction
+function b = isgriddata (X)
+ d1 = diff (X, 1, 1);
+ d2 = diff (X, 1, 2);
+ b = all (d1 (:) == 0) & all (d2 (:) == d2 (1));
+endfunction
+
+## Compute the bicubic interpolation coefficients
+function o = bc(x)
+ x = abs(x);
+ o = zeros(size(x));
+ idx1 = (x < 1);
+ idx2 = !idx1 & (x < 2);
+ o(idx1) = 1 - 2.*x(idx1).^2 + x(idx1).^3;
+ o(idx2) = 4 - 8.*x(idx2) + 5.*x(idx2).^2 - x(idx2).^3;
+endfunction
+
+## This version of sub2ind behaves as if the data was symmetrically padded
+function ind = sym_sub2ind(sz, Y, X)
+ Y (Y < 1) = 1 - Y (Y < 1);
+ while (any (Y (:) > 2 * sz (1)))
+ Y (Y > 2 * sz (1)) = round (Y (Y > 2 * sz (1)) / 2);
+ endwhile
+ Y (Y > sz (1)) = 1 + 2 * sz (1) - Y (Y > sz (1));
+ X (X < 1) = 1 - X (X < 1);
+ while (any (X (:) > 2 * sz (2)))
+ X (X > 2 * sz (2)) = round (X (X > 2 * sz (2)) / 2);
+ endwhile
+ X (X > sz (2)) = 1 + 2 * sz (2) - X (X > sz (2));
+ ind = sub2ind(sz, Y, X);
+endfunction
+
+
%!demo
%! A=[13,-1,12;5,4,3;1,6,2];
%! x=[0,1,4]; y=[10,11,12];
@@ -493,3 +581,7 @@
%! assert(interp2(x,y,A,x,y,'linear'), A);
%! assert(interp2(x,y,A,x,y,'nearest'), A);
+%!test % for Matlab-compatible rounding for 'nearest'
+%! X = meshgrid (1:4);
+%! assert (interp2 (X, 2.5, 2.5, 'nearest'), 3);
+
|
GitWeb