What is seed point?

In the first step, we need to determine some points on neuron before we trace them and sum their length up. Those points are called “seed points”, which by definition are points on or near the center line of a segment of neuron (Zhang et al 2007). Any seed point detection method also need to meet following criteria: 1) at least one seed point is detected on every neuron; 2) the more seed points are detected on a neuron, more accurate the tracing is; 3) two initial directions are used to ensure that the tracing is complete.

 

How to detect seed point?

Our seed point detection consists of two steps. In the first step, we build a grid with N rows and M columns on these images. Rather than researching all the pixels, we find local maxima in all the lines on the grid. In our program, user can change N and M to detect more or less seed points. We use N=15, M=15 by default. The following image (Figure1.1) shows an example of a 15*15 grid.

 

The second step is to filter out non-seed points found in first step due to noise and image artifacts. Through many trials, we found the most accurate way is to remove a candidate if it meet any one of the following conditions:

    1)

    2)

    3) The neighbors of the candidate fail to satisfy that the closer to the candidate, larger average intensity they have.

mu_I is the mean of intensity and sigma_I is the standard deviation of intensity. And DM_p is local difference of means of foreground and background, which is formulated as

and are the mean and variance of all DM in the image. The following image (Figure1.2) shows an example of seed point detection.

 

 

Method Analysis

Through many tests, we find our seed point detection method is better than what is described in Zhang and Mitchel’s paper (Zhang et al 2007), (Mitchel 2013). The difference exist in the thresholds to filter out non seed point candidates. They only used two thresholds, and their SNR threshold (signal-to-noise ratio) remove many real seed points.

The following figure (Figure1.3) is the result of our method. We successfully remove most of points in the background neuron network which we don’t want to count, while we remain nearly all the real seed points.

 

The following figure is result of their method. It’s obvious that they lose lots of real seed points while remain many points in background.

 

However, there are some images really hard for both of the methods to detect seed points. Like the following figure. Its foreground neurons are as thin as the background ones, and they only different at their brightness. Thus, our method detect many seed points we don’t want. But this situation just happens on few cases.

 

A closer look at the background and seed points we found. It is a dense net of neutrons.