x=seq(0, 2*pi,0.1)
y=sin(x)
plot(x,y)
x_i = x
y_i = y
x = x+rnorm(63,0,0.15)
y = y+rnorm(63,0,0.15)
plot(x, y)
x_d = x
y_d = y

for(i in 5:63){
  x[i] = (sum(x_d[(i-4):i] * c(1/20,1/6,1/5,1/4,1/3)))
}

for(i in 5:63){
  y[i] = (sum(y_d[(i-4):i] * c(1/20,1/6,1/5,1/4,1/3)))
}
#x[1:4] = NA
#y[1:4] = NA

plot(x[-(1:4)],y[-(1:4)])


image = image_read(path = "~/Masterarbeit/TeX/Plots/Data/klammern60_80.jpg")
kernel <- matrix(0, ncol = 3, nrow = 3)
kernel[c(1,3),1] = -1
kernel[c(1,3),3] = 1
kernel[2,1] = -2
kernel[2,3] = 2
kernel

kernel <- matrix(data = c(1,4,7,4,1,4,16,26,16,4,7,26,41,26,7,4,16,26,16,4,1,4,7,4,1),
                 ncol = 5, nrow=5)
kernel = kernel/273

n=11
s=4
kernel = matrix(0,nrow = n, ncol = n)
for(i in 1:n){
  for(j in 1:n){
    kernel[i,j] = 1/(2*pi*s) * exp(-(i+j)/(2*s))
  }
}

image_con <- image_convolve(image, (kernel))
image_con
image_write(image_con, "~/Masterarbeit/TeX/Plots/Data/image_conv11.png", format="png")
img <- readPNG("~/Masterarbeit/TeX/Plots/Data/image_conv11.png")


out <- matrix(0, ncol = 15, nrow=20)
for(j in 1:15){
  for(i in 1:20){
    out[i,j] = max(img[((i-1)*4 +1):((i-1)*4+4), ((j-1)*4 +1):((j-1)*4+4)])
  }
}

writePNG(out, target = "~/Masterarbeit/TeX/Plots/Data/image_conv12.png")