Verifying Assumption: Centroid convergence

Now in the first step we are experimenting to find if the centroid is converging to a darker region in side the synapse.

Convergence: The algorithm described in the previous blog was run on the following images:

1. Original image
2. Smoothened image (15x15 Gaussian blur) (GIMP generated)
   
3. Perona-Malik anisotropic diffusion image (MATLAB Central)

In all the images the the centroid converges. The results are shown below.

Convergence of nearby points to Center: The next step is to prove that if taken a point around the synapse it would converge again to the synapse location. To prove this we add some Uniform noise to the Synapse co-ordinate locations and run the algorithm to find out the centroids.

On running it on the third image. The histogram of distance between the original points convergence and the noisy co-ordinates convergence is shown below. The noise levels are 10, 20, 30 pixels



Now looking at the data we see that distance is really really LARGE, more than 50% of pixels is farther than 10 pixels from where the original convergence is. We made an assumption that noise is uniform. Still to go ahead with approach we need to see if the positioning of the SIFT key points is really same as co-ordinates affected by uniform noise. We can attempt to converge the actual SIFT points in the image and then see the number of synapses having SIFT points closer to them hoping that the noisy synaptic locations are not a correct representation of the SIFT key points.