<blockquote>
<p>What I understand from the book and the figure (and I may be wrong) is that everything on the left of the bar is white (stimulus is present) and everything at the right of ithe bar is black (no stimulus).</p>
</blockquote>
<p>Yes, I believe this interpretation is correct.</p>
<p>If everything left/above the bar is white, P is on, because there is light on its center and it's an on-center cell (=active with light on center). If everything right/below the bar is dark, Q is on, because there is dark on it's center and it's an off-center cell (=active with dark on center). This tells us there is an edge here.</p>
<p>I think you're probably overestimating the importance of the surround here, or not appreciating that neurons can have a range of activity levels, where even small changes in activity are useful and meaningful in the brain. With the edge across the receptive field of P, P is going to fire more than it would if the entire cell was illuminated; as drawn, part of P's off-surround is not getting light. Same for Q, if all of Q was dark, it would fire less than in this situation, where part of Q's on-surround is illuminated, while its center is dark.</p>
<p>If you have a bunch of these cells, like in (b), you can easily see the extent of the edge.</p>

CC BY-SA 4.0
2022-08-30T14:58:21.303Z
2022-08-30T14:58:21.303Z
Bryan Krause
<p>I'm currently reading the excellent book &quot;Vision&quot; by David Marr. In chapter 2.2 (ZERO-CROSSINGS AND THE RAW PRIMAL SKETCH), he explains a possible model for the physiological detection of zero-crossings.
As <em>zero-crossing</em> we mean the locations of the image where the laplacian is zero (that represents a sudden change in intensity, i.e. an edge)</p>
<p><a href="https://i.sstatic.net/KGtJm.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/KGtJm.jpg" alt="enter image description here" /></a></p>
<p>From Marr's book:</p>
<blockquote>
<p>From a physiological point of view, zero-crossing segments are easy to detect without relying on the detection of zero values, which would be a physiologically implausible idea. The reason is that just to one side of the zero-crossing will lie a peak positive value of the filtered image ∇2G * I, and just to the other side, a peak negative value. These peaks will be roughly w2–D/ apart, where w2–D is the width of the receptive field center of the underlying filter ∇2G. Hence, just to one side, an on-center X cell will be firing strongly, and just to the other side, an off-center X cell will be firing strongly; the sum of their firings will correspond to the slope of the zero-crossing—a high-contrast intensity change producing stronger firing than a low-contrast change. The existence of a zero-crossing can therefore be detected by a mechanism that connects an on-center cell and an off-center cell to an AND gate,* as illustrated in Figure 2–18(a).</p>
</blockquote>
<p>Marr, David. Vision (pp. 93-94). MIT Press. Kindle Edition.</p>
<p><a href="https://i.sstatic.net/MDbkt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/MDbkt.png" alt="enter image description here" /></a></p>
<p>I'm not quite able to fully understand why this would make sense since</p>
<ol>
<li>The receptive field of P (on-center ganglion cell) is stimulated even on its periphery (and this would reduce its firing)</li>
<li>The receptive field of Q (off-center ganglion cell) isn't stimulated on its periphery (and this would reduce its firing too, right?)</li>
</ol>
<p>This is the kind of stimulus I guess it's being represented by the book:</p>
<p><a href="https://i.sstatic.net/0QIdi.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/0QIdi.png" alt="enter image description here" /></a></p>
<p>Are these reasonable doubts or did I not fully understand Marr's model?</p>
<p>To note, in <a href="https://www.youtube.com/watch?v=ePP0G7FJGPI" rel="nofollow noreferrer">this</a> video by Nancy Kanwisher from MIT, she explains a physiological model for edge detection (not necessarily zero-crossings detection) in a different way which makes way more sense to me:</p>
<p><a href="https://i.sstatic.net/ZW0mI.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZW0mI.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2022-08-29T07:16:41.340Z
$Q$ is an off-center cell and so it is activated in the periphery.
vkehayas
CC BY-SA 4.0
2022-08-29T07:46:43.313Z
Hi @vkehayas, thanks for your responde. Why should it be activated? off-center ganglion cells fire when they receive a light stimulus on their surround (as explained [here](https://www.cns.nyu.edu/~david/courses/perception/lecturenotes/ganglion/ganglion.html), the image should be pretty clear), and in this case the surround of Q is mainly dark.
ИванКарамазов
CC BY-SA 4.0
2022-08-29T08:09:13.303Z
You are misinterpreting the definition of an off-center cell. Off-center cells fire when their surround is stimulated and are inactivated when their center is stimulated. In the example above, the stimulus --the bar-- is on the surround of the cell's RF.
vkehayas
CC BY-SA 4.0
2022-08-29T09:29:07.487Z
What I understand from the book and the figure (and I may be wrong) is that everything on the left of the bar is white (stimulus is present) and everything at the right of ithe bar is black (no stimulus). Given this premise, I agree that the center of Q (off-center) isn't stimulated (since it's black), but its sourround should be minimally activated since there shouldn't be much light (other than a little portion light around the bar). If this isn't clear maybe I'll try to do a little illustration to express my reasoning once I'll be home.
ИванКарамазов
CC BY-SA 4.0
2022-08-30T07:19:48.237Z
@vkehayas I updated the question with an illustration
ИванКарамазов
<neuroscience><cognitive-neuroscience><vision>
Doubt about zero-crossings detection in the visual system
ИванКарамазов
# Doubt about zero-crossings detection in the visual system

(Asked by: username_0 on 2022-08-27)

I'm currently reading the excellent book "Vision" by David Marr. In chapter 2.2 (ZERO-CROSSINGS AND THE RAW PRIMAL SKETCH), he explains a possible model for the physiological detection of zero-crossings.
As *zero-crossing* we mean the locations of the image where the laplacian is zero (that represents a sudden change in intensity, i.e. an edge)

[![enter image description here](https://i.sstatic.net/KGtJm.jpg)](https://i.sstatic.net/KGtJm.jpg)

From Marr's book:

> From a physiological point of view, zero-crossing segments are easy to detect without relying on the detection of zero values, which would be a physiologically implausible idea. The reason is that just to one side of the zero-crossing will lie a peak positive value of the filtered image ∇2G \* I, and just to the other side, a peak negative value. These peaks will be roughly w2–D/ apart, where w2–D is the width of the receptive field center of the underlying filter ∇2G. Hence, just to one side, an on-center X cell will be firing strongly, and just to the other side, an off-center X cell will be firing strongly; the sum of their firings will correspond to the slope of the zero-crossing—a high-contrast intensity change producing stronger firing than a low-contrast change. The existence of a zero-crossing can therefore be detected by a mechanism that connects an on-center cell and an off-center cell to an AND gate,\* as illustrated in Figure 2–18(a).

Marr, David. Vision (pp. 93-94). MIT Press. Kindle Edition.

[![enter image description here](https://i.sstatic.net/MDbkt.png)](https://i.sstatic.net/MDbkt.png)

I'm not quite able to fully understand why this would make sense since

1. The receptive field of P (on-center ganglion cell) is stimulated even on its periphery (and this would reduce its firing)
2. The receptive field of Q (off-center ganglion cell) isn't stimulated on its periphery (and this would reduce its firing too, right?)

This is the kind of stimulus I guess it's being represented by the book:

[![enter image description here](https://i.sstatic.net/0QIdi.png)](https://i.sstatic.net/0QIdi.png)

Are these reasonable doubts or did I not fully understand Marr's model?

To note, in [this](https://www.youtube.com/watch?v=ePP0G7FJGPI) video by Nancy Kanwisher from MIT, she explains a physiological model for edge detection (not necessarily zero-crossings detection) in a different way which makes way more sense to me:

[![enter image description here](https://i.sstatic.net/ZW0mI.png)](https://i.sstatic.net/ZW0mI.png)

**Tags:** neuroscience, cognitive-neuroscience, vision

> **Comments:**
> **username_1**: $Q$ is an off-center cell and so it is activated in the periphery.  
> **username_0**: Hi @username_1, thanks for your responde. Why should it be activated? off-center ganglion cells fire when they receive a light stimulus on their surround (as explained [here](https://www.cns.nyu.edu/~david/courses/perception/lecturenotes/ganglion/ganglion.html), the image should be pretty clear), and in this case the surround of Q is mainly dark.  
> **username_1**: You are misinterpreting the definition of an off-center cell. Off-center cells fire when their surround is stimulated and are inactivated when their center is stimulated. In the example above, the stimulus --the bar-- is on the surround of the cell's RF.  
> **username_0**: What I understand from the book and the figure (and I may be wrong) is that everything on the left of the bar is white (stimulus is present) and everything at the right of ithe bar is black (no stimulus). Given this premise, I agree that the center of Q (off-center) isn't stimulated (since it's black), but its sourround should be minimally activated since there shouldn't be much light (other than a little portion light around the bar). If this isn't clear maybe I'll try to do a little illustration to express my reasoning once I'll be home.  
> **username_0**: @username_1 I updated the question with an illustration  

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## 1 answers

### Answer by username_2 on 2022-08-30. Score: 1

> What I understand from the book and the figure (and I may be wrong) is that everything on the left of the bar is white (stimulus is present) and everything at the right of ithe bar is black (no stimulus).

Yes, I believe this interpretation is correct.

If everything left/above the bar is white, P is on, because there is light on its center and it's an on-center cell (=active with light on center). If everything right/below the bar is dark, Q is on, because there is dark on it's center and it's an off-center cell (=active with dark on center). This tells us there is an edge here.

I think you're probably overestimating the importance of the surround here, or not appreciating that neurons can have a range of activity levels, where even small changes in activity are useful and meaningful in the brain. With the edge across the receptive field of P, P is going to fire more than it would if the entire cell was illuminated; as drawn, part of P's off-surround is not getting light. Same for Q, if all of Q was dark, it would fire less than in this situation, where part of Q's on-surround is illuminated, while its center is dark.

If you have a bunch of these cells, like in (b), you can easily see the extent of the edge.


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