Computer Vision (22) and Optics

If I take a point source and place it in space it would emit light spherically in all directions around it. You will be able to see a point, only if the rays from that point reach your eyes. This means that you will be able to see a point source from any place around it. If u just had a sensor (retina) and not the lens in your eye, these rays that are diverging and almost everywhere in space would fall all over the retina to form an image which would be a uniform light patch in your brain. The same applies to non light sources as well. You will be able to see an object only if the object is reflecting light in the direction you are seeing. Again an object can reflect light in almost any direction around it. Without the lens, the reflected light from many points around you can fall at the same place on the retina as shown below.

The intensity and frequency of the reflected light from these various points can be different and hence get summed up at a point on the retina. This scenario can happen for every pixel on the sensor and hence the image that you will get will just be the summation of the intensities and frequencies of the rays coming out from various points around you. As a result of this you will always end up with a uniform patch of light on the sensor if you try to take an image without a lens.

If you didn’t have a lens in your eyes, you would only be able to know the amount of light present in the surrounding and not the objects present in front of you. The various objects wouldn’t be distinguishable at all.

To see a point as a point, we need to converge the rays that are diverging from it, to a point again. The lens does exactly this. Your brain sees various objects around it as they are because your eye lens converge the rays coming from it on the retina.

Computer Vision (21) and Optics

Let's first understand what focus or accommodation is. We have been learning since our school days that light is a ray, wave, particle, it has a dual nature, etc, etc. And lately we have also known the famous and undebatable theory on light by Richard P Feynman et al, that the dual nature of light can be explained by considering light as a particle having an instantaneous phase (which gives it the properties of a wave) associated with it. This theory is called the QED; Quantum Electro Dynamics and it promises to combine the particle and wave theories of light into one single entity that can explain almost all phenomenon of light to its highest possible accuracy. Interested people can read his own book called "QED: The Strange Theory of Light and Matter", which has his famous lectures.

But why am saying all this? When I focus light, I am bringing together light from a region to a point and to analyze this I need to decide on the theory. For now I will not get into the complex QED, but will try to justify my experiments with simple ray diagrams. Will come to QED after some more posts.

Imagine that we did not have eye ball or in other words the lens of our eyes, but just had the retina to capture the light from the surrounding. How would the surrounding appear to you? There is one way to experiment this (ofcourse not by removing the lens of your eyes :)). If you have a webcam just try removing the lens of it and switch it on exposing the retina, sorry the sensor to the surrounding. What do you see?

Photography and Travel

Kumara Parvatha, also known as KP is one of the tallest peaks in Karnataka. It is a real challenge to trek this in a day. The interesting part is that you can get down from a different route to the one you took to climb. This makes the trek even more interesting. This photo was taken at the top, where we reached a bit late in the morning (the next day we started to climb :( ). Never the less it is heaven out there at any time. This place is situated near subramanya. You can get more info on it here: http://www.kumaraparvathaconquered.blogspot.com

Computer Vision (20)

Even though a lot of people believe that a stereogram is exactly equivalent to seeing with both the eyes there is one major difference. Stereograms are generally shot by moving the camera horizontally by a short distance (in case of a single camera system) or by keeping two cameras side by side, which capture the horizontal disparity. Suppose there are two infinitely long horizontal bars, one at a certain distance from the other (both horizontally and vertically) and nothing else around it and you take a stereo image of this, with the camera taking the projection of their lengths, you will fail to capture the horizontal disparity, because there is none in this direction.

A camera takes the horizontal projection of objects (horizontal line pointing towards you), and so the distance between the horizontal bars along this direction cannot be shown in this 2D image. The vertical distance between them is ‘v’. In other words, if we try to capture this 3D setup in a stereo image pair to get the horizontal depth between the bars you will end up with exactly the same image in the left and right. There is no use seeing it stereoscopically, because, which point in the two images will the brain correspond? Since the camera is moved horizontally, the vertical distance between the two bars remains the same in the stereo image.

In a real scenario, how do our eyes and brain together manage to catch the right point? I mean, form a triangle and get the depth out of it. This is possible because, in addition to just 2D projection our eyes collect in real time one more parameter; focus. Focus is exactly the same as accommodation that I was describing in monocular cues. Our eye has to accommodate itself to focus (see sharply) objects at different depths. When object at one depth is seen sharply depending on the aperture of our eyes objects at other distance will be blur. This means that focus or accommodation is dependent on depth and unique for every distance from the eye. So the accommodation value would actually give the absolute depth of them object.

Photography

To give the readers a change from the technical stuff I had thought of posting some other things also, so here it is. This is a place called Devarayana Durga in Tumkur around 70 Km from Bangalore. Its a nice place to visit for a day, but it was already 4 when we left Bangalore and so reached there just right at the sunset. Managed to capture the last few glimpses of the sun for that day. If you guys plan to go there better leave a bit early.

Computer Vision (19)

Disparity is a must to perceive depth in a stereoimage pair and so our brain needs at least two separated points with disparity to extract the distance between them. Disparity at a later stage would use triangulation to perceive depth, but this triangle would depend on the separation between the images and not the depth of the actual object. The below image illustrates triangulation from disparity when a stereogram is cross viewed.

The red lines are traced when the eyes combine the rectangle and the green lines when they combine the circle. The point of intersection of the red lines gives the 3D location of the rectangle and the green lines that of the circle. As mentioned earlier the circle is in front of the rectangle when cross viewed. One of the points for the formation of the triangle comes from the point of intersection of either the red or the green lines and the other two points are the two eyes. The distance of the point of intersection of lines from the two eyes (d), depends on the separation between the images, so the absolute distance of the objects remains unknown in the stereo image pair. The relative depth of different objects from one another is obtained by corresponding objects form the two images, which moves the point of intersection of the lines according to the 3D placement of the objects (similar to red and green lines).

This is not the case when we extract depth from the actual 3D surrounding because our eye makes use of triangulation from the convergence of the eyes and not disparity. Our eyes assist to perceive the absolute depth of our surrounding while in stereograms we can only perceive the relative depth of one object from the other.

Computer Vision (18)

Disparity is something that is required to perceive depth from 2D stereo image pairs. For example, to create a stereo image pair in a computer as shown below, I just placed a rectangle and a circle one beside the other in the left image, copied the same thing for the right image as well, and then increased the distance between the rectangle and the circle in the right image.

The 3D interpretation of it is as follows. The image seen below is the top view of the 3D space whose 2D projection is shown above. On cross viewing it, you would see the circle in front of the rectangle. Cross viewing a stereogram means, your left eye would see the image on the right and your right eye the one on the left.

The dotted lines are the angle of view of the eyes (not to scale). The blue lines are the projection lines of the objects on the respective eyes. Since the eyes are placed at some distance from one another the projection of the objects in 3D space will always be different on both the eyes, except when the objects are on the vertical bisector. This difference in the projection lengths is what disparity is.

Disparity = length of the red line - length of the green line.

From the diagram it is clearly evident why the distance between the rectangle and the circle in the right image (red line) is kept greater than the left image (green line) to recreate this 3D effect in the brain when viewed stereoscopically. Think about how the gap should be to view the circle behind the rectangle.