%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Kernels for gradient integration (Section 4)                     
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  - Low budget set (F_5,3)

F = [0.15 0.5 0.7 0.175 0.547]  

h1 = [F1 F2 F3 F2 F1]
h1 = h1^T * h1

h2 = h1

g = [F4 F5 F4]
g = g^T * g

%%  - High budget set (F_7,5)

F = [0.06110 0.26177 0.53034 0.65934 0.51106 0.05407 0.24453 0.57410];

h1 = [F1 F2 F3 F4 F3 F2 F1]
h1 = h1^T * h1

h2 = h1 * F[5]

g = [F6 F7 F8 F7 F6]
g = g^T * g


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Kernels for membrane interpolation (Section 5)                     
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

F = [ 0.1507146 0.6835785 1.0334191 0.0269546 0.0311849 0.7752854 ]

h1 = [F1 F2 F3 F2 F1]
h1 = h1^T * h1

h2 = h1 * F[4]

g = [F5 F6 F5]
g = g^T * g


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Kernels for Gaussian filters (Section 6)                     
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Sigma 2: F = [0.7339 0.2630 0.6192 0.9755 1.1288 0.4513 0.5085 1.9416 23.0125 -9.3658 3.1551 0.6842]
Sigma 4: F = [2.3828 0.4974 0.9159 1.6206 1.9186 -0.1901 -2.3554 1.9836 -1.4251 1.4640 2.0900 -0.0215]
Sigma 6: F = [2.9151 0.1720 0.6809 1.8451 2.4898 0.3255 0.0319 -0.1333 0.2287 6.7394 -0.0132 0.0015]
Sigma 8: F = [5.7838 0.3108 0.3825 0.9631 0.9048 -3.3178 3.1805 -1.9044 2.2705 9.0461 -0.2984 0.0325]
Sigma 10: F = [4.8964 0.0296 0.2732 1.5194 2.5687 -0.1105 0.0992 -0.0962 8.9006 0.0535 -0.0069 0.0008]
Sigma 12: F = [23.0257 0.0090 0.0455 0.1144 0.1612 0.0243 -0.0817 0.2276 18.3173 1.1993 -2.9933 1.9567]
Sigma 14: F = [10.0403 0.1000 0.2523 0.5464 0.6764 0.9436 -1.3376 1.4448 11.3074 -0.4674 0.1386 -0.0345]
Sigma 16: F = [11.1001 0.1434 0.2505 0.5329 0.6051 2.1853 -3.2955 3.3579 9.1042 -0.8763 0.2936 -0.0759]
Sigma 18: F = [20.5402 0.0457 0.0665 0.1444 0.1524 1.6428 -4.5349 8.3187 18.2215 -4.7240 3.2388 -1.5945]
Sigma 20: F = [4.8840 0.0630 0.4203 2.1948 3.7092 1.1879 -1.2909 14.3321 0.1261 -0.0125 0.0042 -0.0005]

h1 = [1 4 6 4 1]/16.0;
h1 = h1^T * h1

h2 = h1 * F[1] 

g = [F2 F3 F4 F5 F4 F3 F2]
g = g^T * g

w^l, for l=1:7
[F6 F7 F8 F9 F10 F11 F12]