Recent content by emmasaunders12

Thanks essentially I have been told that the function (v) is constrained to be in the space of diffeomorphisms by ensuring the norm of the velocity field is regularized with a differential operator from fluid mechanics to ensure the transformation lies in the space of differmorphisms. Does this...

Would be great if you can assist in helping me understand how to find the sobolev norm of a function, I am not even sure how to start?

Hi its a vector field for image registration, but apparently the solobev norm allows it to be in the space of diffeomorphisms

That's a very simple explanation thanks, how does one calculate the sobolev norm of a function and if a function fits within a sobolev space what does that tell us about the function?

Thanks, image registration, so how can you ensure that a function has a sobolev structure and hence a sobolev norm?

Can someone give me in very abstract terms what a sobolev norm is or means?

Hi I am using a convolution neural network (with inversion) to simulate images with the same "texture" as the input image, using a random image to start with. The activations of the CNN are first learned with an example or source image. A cost function then minimizes the difference between the...

The specific problem is described on page 4 here https://arxiv.org/pdf/1505.07376v3.pdf

Thanks for the response, its the loss function of a neural network, so I've corrected to G and Gest, primes refer to transpose

Could someone please help me work through the differentiation in a paper (not homework), I am having trouble finding out how they came up with their cost function. The loss function is L=wE, where E=(G-Gest)^2 and G=F'F The derivative of the loss function wrt F is proportional to F'(G-Gest)...

ok what if the added info is that the origin point is (0,0) and the line to the "midpoint" must be perpendicular

Thanks for the reply, yes its a regular octagon, your correct in stating that the lines won't pass through the centre and I need to figure out the deviation from the centre at the midpoint of the line that connects two faces

Hi perhaps someone can point me in the correct direction. If I have an Octagon and the co-ordinates of two points on separate faces, example, face 1 (xo,yo) and face 2 (x1,y1). And I draw a straight line connecting the two points. How can I calculate the radial distance to the midpoint of...

Hi Madness, yes certain elements of the data matrix and hence eigenvectors are considered to be zero, is this equivalent to a submanifold in comparison to the full manifold when the zeros were not present?

Thanks madness for clarifying, this is where my initial confusion lies, if PCA learns the space don't the eigenvectors define the manifold, as new data projected into it will fall in a different position are you stating though that this would then however be a new manifold. One final point...