Why does the egg thin appear completely white in one of these? I cant think of a reason that it would appear entirely like that.
If I had to guess, I'd say it's something to do with light bouncing around inside the glass egg taking a certain number of bounces to be directed at the camera - when just paying attention to photons of this many bounces, it would look more or less like the light is being reflected by a mirror.
For context, this slide comes from page 325 of Veach's thesis in Chapter 10: Bidirectional Path Tracing. (He received a technical Academy Award for this thesis btw.)
Quoting the caption for this figure: "Each row r shows the contributions of the sampling
techniques for a particular path length k = r + 1. The position of each image in its row
indicates how the paths were generated: the s-th image from the left in each row uses s
light subpath vertices, while the t-th image from the right uses t eye subpath vertices.".
k = r + 1
Now, in the first row, the egg is completely black. This is because there are not enough bounces for light to travel from a source to the egg and straight to the camera. Pretty straight forward.
In the second row, the egg starts to reflect light.. at least in some of the images. The left most image in this row is a result of creating a light path from the camera, to the egg, and then to a diffuse point on the wall; this is then connected directly to the light source.
However, there are certain images where the egg is completely black. Besides row 1, the egg is black in image 2, row 2; image 3, row 3; and image 4, row 4. In these images, bidirectional path tracing produces an "eye subpath" that consists of two vertices: the camera vertex and a point on the egg. Because the egg is specular, connecting this point on the egg to any other light subpath is always going to produce 0 contribution.
And this is precisely why different light path sampling strategies is important. If we consider each image shown in this slide as being a different sampling strategy, some strategies are more effective of generating light paths than others. If we stick to the one strategy used in image K, row K, then the egg would appear pitch black no matter how many samples we throw at our scene.