Yay! I think you’re right. This seems to work.
Here’s a final MWE:
using Plots, Dierckx
image_x = [i + (rand()-.5)/4 for i in 1:10, j in 1:10]
image_y = [j + (rand()-.5)/4 for i in 1:10, j in 1:10]
plot(image_x,image_y, marker=:circle,color=:black)
plot!(image_x',image_y',color=:black,legend=false, grid=false)
x_in = [rand(1.5:9.5) + (rand()-.5)/2 for i in 1:10]
y_in = [rand(1.5:9.5) + (rand()-.5)/2 for i in 1:10]
scatter!(x_in,y_in,marker=:circle,color=:red)
png("a1.png")
world_x = linspace(125,300,10)
world_y = linspace(-5,53,10)
A = vec(world_x .+ 0world_y')
s = Spline2D(vec(image_x), vec(image_y), A, s = 100.)
x_out = evaluate(s, x_in, y_in)
A = vec(0world_x .+ world_y')
s = Spline2D(vec(image_x), vec(image_y), A, s = 100.)
y_out = evaluate(s, x_in, y_in)
x = repmat(world_x,1,10)
y = repmat(world_y',10)
plot(x,y, marker=:circle,color=:black)
plot!(x',y',color=:black,legend=false, grid=false)
scatter!(x_out, y_out, marker=:circle,color=:red)
png("a2.png")
and the two resulting images:
Thanks @TsurHerman!