How to do Bilinear Interpolation using JMP?

smostafa — Thu, 17 Jan 2019 02:19:24 GMT

Essentially it is called 2D multivariate interpolation. I have set of locations (x,y) and a corresponding data eg: z=color value. For some of the (x,y) the z column has data missing. I want to use the nearest two known ( x1,y1,z1) and (x2,y2,z2) to interpolate the value for (x3,y3, z3=?).

Theoretically this wiki/Bilinear_interpolation is what I like to get.

Does JMP has a way of doing this?

Also I need first group the X,Y data by two other column A,B. Example. COl A,B represents filename and frame number. X,Y is the location of a pixel in the frame and Z is the pixel color.

I want to interpolate the Z value for missing pixels in each frame in each file.
Sample Data set

File	Frame	X	Y	Color
Antman	1	0	0	255
Antman	1	5	5	195
Antman	1	3	2	??
Antman	2	0	0	255
Batman	3	0	0	255
Batman	3	3	2	??
Batman	3	5	5	100

Re: How to do Bilinear Interpolation using JMP?

ian_jmp — Thu, 17 Jan 2019 16:16:34 GMT

If I understand correctly, you will need four points (not two) for the bilinear interpolation. The grouping columns would be wasily dealt with, so for one group you could do something like:

Names Default To Here( 1 );

// Example table: Four complete observations, and one missing 'Colour' to be
// obtained by bilinear interpolation
dt = New Table( "Antman_1",
			Add Rows( 5 ),
			New Column( "X",
				Numeric,
				"Continuous",
				Format( "Best", 12 ),
				Set Values( [0, 5, 3, 5, 0] )
			),
			New Column( "Y",
				Numeric,
				"Continuous",
				Format( "Best", 12 ),
				Set Values( [0, 5, 2, 0, 5] ),
				Set Display Width( 92 )
			),
			New Column( "Colour",
				Numeric,
				"Continuous",
				Format( "Best", 12 ),
				Set Values( [255, 195, ., 100, 150] )
			)
		);

// Using the notation at: https://en.wikipedia.org/wiki/Bilinear_interpolation
x1 = dt[1, "X"];
x2 = dt[2, "X"];
y1 = dt[1, "Y"];
y2 = dt[2, "Y"];
q11 = dt[1, "Colour"];
q21 = dt[4, "Colour"];
q12 = dt[5, "Colour"];
q22 = dt[2, "Colour"];
x = dt[3, "X"];
y = dt[3, "Y"];

// Interpolate in the X direction
r1 = Interpolate(x, x1, q11, x2, q21);
r2 = Interpolate(x, x1, q12, x2, q22);

// Interpolate in the Y direction
p = Interpolate(y, y1, r1, y2, r2);
Wait(3);
dt[3, "Colour"] = p;

This is unlikely to be the 'best' way, but to do better some sample data (in a JMP table) would be required. You would also need to decide how to handle edge cases.

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How to do Bilinear Interpolation using JMP?

Re: How to do Bilinear Interpolation using JMP?