I thought it was interesting that most people thought the sun would have the higher norm. It's obviously "brighter" but a norm could be defined in ways that doesn't favor having a giant fireball in the middle of the picture
bpx
@ibuildrobots I think a lot of people may have considered each pixel as an RGB vector, and therefore the picture is actually a vector of vectors. Taking the L2 norm of a pixel does correspond to brightness, but I know I was considering the amount of "white" in the picture which would be RGB(256, 256, 256). This was interesting because we collectively considered "brighter" as the larger norm, but since the picture is a vector of vectors, we actually took the norm of the picture w.r.t the norm of the individual pixels.
keenan
@ibuildrobots Yes, absolutely. Or for instance, if we consider a norm that measures the length of edges in the image (as we did later on), it may be that there are more edges in the cave image than the sun image. That's an important part of understanding the place of norms and inner products in applications: there's not one "true" inner product, but rather many different inner products you could pick for various tasks. (Likewise, many different gradients---which depend on the choice of inner product.)
keenan
@bpx Yep, very good point. In order to define a norm on images, we may also have to define a norm on color values. There are actually many different color spaces we could choose, and the norm in RGB space is actually not the preferred norm for many tasks, like image compression. (Here one might use, say, the XYZ color space rather than RGB.) We'll have a whole lecture on color later on.
I thought it was interesting that most people thought the sun would have the higher norm. It's obviously "brighter" but a norm could be defined in ways that doesn't favor having a giant fireball in the middle of the picture
@ibuildrobots I think a lot of people may have considered each pixel as an RGB vector, and therefore the picture is actually a vector of vectors. Taking the L2 norm of a pixel does correspond to brightness, but I know I was considering the amount of "white" in the picture which would be RGB(256, 256, 256). This was interesting because we collectively considered "brighter" as the larger norm, but since the picture is a vector of vectors, we actually took the norm of the picture w.r.t the norm of the individual pixels.
@ibuildrobots Yes, absolutely. Or for instance, if we consider a norm that measures the length of edges in the image (as we did later on), it may be that there are more edges in the cave image than the sun image. That's an important part of understanding the place of norms and inner products in applications: there's not one "true" inner product, but rather many different inner products you could pick for various tasks. (Likewise, many different gradients---which depend on the choice of inner product.)
@bpx Yep, very good point. In order to define a norm on images, we may also have to define a norm on color values. There are actually many different color spaces we could choose, and the norm in RGB space is actually not the preferred norm for many tasks, like image compression. (Here one might use, say, the XYZ color space rather than RGB.) We'll have a whole lecture on color later on.