Edge Detection
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Latest revision as of 08:04, 4 August 2005
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Contents |
Intro
Independently of the group in Texas, we also came to this idea in a discussion during lunch: the classical Edge Detection problem. Rather simple in computer science, but hopefully new to the biology community (well, it seems it isn't).
Principle
In computer vision you typically want to make out the contours of an object or region. At the contour or edge something changes significantly, i.e. there is a strong gradient of color or lighting (e.g. the red car standing in front of the blue garage will have both). Edge Detection algorithms make it possible to find those changes and to draw a line corresponding to existing contours.
The "AND" approach
Basic Idea
One could imagine a population to react to light so that some product A is produced while another possible product B is suppressed, and vice versa in darkness. Also, one could imagine that those products, A or B, do not diffuse very far (or are quickly degenerating). Thus, when a pattern is projected on a population there will be sharp gradients between the lighted area and the one in darkness. Now let's assume that the presence of both products, A and B, are needed, to trigger a third product C, e.g. green fluorescent protein (GFP). Then only the edge will show a change as a fluorescent thin line and biological Edge Detection has been achieved.
possible Extensions
overcome the "a grid is not an edge" problem
the problem
If you project a fine regular grid (light and dark) onto the bacteria, the light and the dark areas are quite close. If the distances between the to areas are small compared to the diffusion lenght, A and B would be (almost) uniformly distributed on the whole area. That means that A and B are present everywhere, leading to the production of C on the whole picture. So the bacteria will "think" that the whole grid is an edge, an obviously (at least from a Computer Science point of view) undesirable behaviour.
possible fix
One can introduce to new genes. One of them produces C when light is irradiated, whereas the other produces D when it's dark. C is repressing the production of B, and D is repressing the production of A.
So when you project a grid on these "enhanced" bacteria, C and D will diffuse through the whole grid, preventing A and B from being produced, and the area won't get fluorescent. If the grid cells are large enough, on a lighted cell, there will be a region where no D is present, so A will be produced there, and analogous on the dark cells.
When A and B have larger diffusion coefficients than C and D, A and B will diffuse out of the light resp. dark cells, so that they are both present at the edge between the two cells. That lead to a correct detection of edges separating areas of sufficient size.
Of course, the determination of all the diffusion coefficients is very crucial! This will add hard difficulties to the implementation of this approach. But there seems to be a cool reward: Because difussion coefficients are depending on temperature, one could imagine to control the resolution of the edge detection device by setting the temperature of the culture medium.
The "medium concentration" approach
In this approach, we are only using one messager A. A is expressed strongly if there is much light shining on a bacterium, and is weakly expressed if the bacterium is not much irradiated. The fluorescent product C, to stick to the notation above, is only produced when the concentration of A is in a medium range.
Given a picture projected onto the bacteria which is very dark on the left hand side, and bright on the right hand side, with a very steep gradient in the middle (i.e. a sharp edge), the bacteria on the left will produce no or little A, whereas the bacteria on the right hand side produce much A. The concentration of A will of course not have a sharp edge on the boundary, but will be blurred due to diffusion. So there is a band with medium concentration of A, resulting in bacteria producing GFP marking an edge.
Discussion
>> for comments, questions and temporary remarks go to the Talk:Edge_Detection
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