Let's consider I have a neural network with one single output neuron. To outline the scenario: the network gets an image as input and should find one single object in that image. For simplifying the scenario, it should just output the x-coordinate of the object.
However, since the object can be at various locations, the network's output will certainly have some noise on it. Additionally the image can be a bit blurry and stuff.
Therefore I thought it might be a better idea to have the network output a gaussian distribution of the object's location.
Unfortunately I am struggling to model this idea. How would I design the output? A flattened 100 dimensional vector if the image has a width of 100 pixels? So that the network can fit in a gaussian distribution in this vector and I just need to locate the peaks for getting the approximated object's location?
Additionally I fail in figuring out the cost function and teacher signal. Would the teacher signal be a perfect gaussian distribution on the exact x-coordination of the object? How to model the cost function, then? Currently I have a softmax cross entropy or simply a squared error: network's output <-> real x coordinate.
Is there maybe a better way to handle this scenario? Like a better distribution or any other way to have the network not output a single value without any information of the noise and so on?