Do we have to use more complex methods to determine relationships between pictures that have semantic relationships, rather then purely graphical. Perhaps the dog picture is not a great example, but one could imagine a color photo of a different horse, and the need for a program that would tell you how similar the horse and position of the horse was.
Animagus
In this situation we could come up with all the different methods, like the hue of the picture, texture, edges... But all those features of an image would be described as vectors, matrices or functions whatever. The way we calculate those representations still based on the linear algebra. Don't know if this explained the your concerns.
keenan
@mhofmann Yes, absolutely. Computationally analyzing semantics of images is of course much more challenging (but also more meaningful) than comparing simple norms like $L^2$. But even here, one often tries to extract features from an image that can still be compared using simple norms like the Euclidean norm (because at the end of the day, that's much more efficient computationally). For instance, you might reduce an image to a histogram of different colors or intensities---the process of converting an image to a histogram is nonlinear and slow, but once you've recorded the histograms for all the images, you can go back to comparing them as good old-fashioned vectors (just a list of numbers per histogram). Beyond simple histograms, computer vision studies local feature descriptors that try to capture important features of an image, like edges and so forth---one classic example is SIFT.
Do we have to use more complex methods to determine relationships between pictures that have semantic relationships, rather then purely graphical. Perhaps the dog picture is not a great example, but one could imagine a color photo of a different horse, and the need for a program that would tell you how similar the horse and position of the horse was.
In this situation we could come up with all the different methods, like the hue of the picture, texture, edges... But all those features of an image would be described as vectors, matrices or functions whatever. The way we calculate those representations still based on the linear algebra. Don't know if this explained the your concerns.
@mhofmann Yes, absolutely. Computationally analyzing semantics of images is of course much more challenging (but also more meaningful) than comparing simple norms like $L^2$. But even here, one often tries to extract features from an image that can still be compared using simple norms like the Euclidean norm (because at the end of the day, that's much more efficient computationally). For instance, you might reduce an image to a histogram of different colors or intensities---the process of converting an image to a histogram is nonlinear and slow, but once you've recorded the histograms for all the images, you can go back to comparing them as good old-fashioned vectors (just a list of numbers per histogram). Beyond simple histograms, computer vision studies local feature descriptors that try to capture important features of an image, like edges and so forth---one classic example is SIFT.