vishwa91
commented
1 year ago Great question! To answer that, let us take a simpler example. Let us say we are given several pairs of points $(x_k, y_k)$. If we were asked to find a continuous function that relates $y_k$ to $xk$, we would perform polynomial fitting of the form, $y = {\sum{q=0}}^Q a_q x^q$. Here, the learnable parameters are $\theta={a_0, a_1, \cdots, aQ}$. However, we can also learn a neural network representation, $y = \mathcal{N}\theta(x)$, where $\mathcal{N}$ is a multilayer perceptron and $\theta$ are its parameters.
In a similar manner, images can also have a continuous function to represent them. In such a case, we have, $i_{(x,y)}=\mathcal{N}_\theta(x,y)$, where $i_{(x,y)}$ is the intensity at the coordinate $(x, y)$. this is an implicit representation with a neural network, and hence the name, ``implicit neural representation (INR)".
If the INR has sufficient capacity, then the image is represented very accurately. MLPs equipped with the traditional nonlinearity such as ReLU however does not have sufficient capacity (think of it as similar to a low-order polynomial). In contrast, nonlinearities such as SIREN (sinusoidal) perform well, but do not scale well to very large signals (think gigapixel images). This is where MINER comes into the picture, by performing a partition of the space into disjoint blocks, and using small MLPs for each block -- somewhat similar to splines instead of a single polynomial. Hence, the capacity of a network architecture can be evaluated well by fitting an image.
Hope that helps!
Net-Maker
Hello, Thanks for yout excllent work! I am an undergraduate student.And i am learning INRs(Implicit Neural Representations) now. I found image fitting task in the experiment part in a lot of INR papers.So i search this task in google but got nothing. could you explain the meaning of this part experiment?It would help me a lot. I wonder is it a way to show the superiority of the INR?Or it's a challenge of INR?Why set this experiment? Best wishes. Looking forward to your reply.