Image recognition
The general neural networks are used for image recognition, not for pin pointing details in an image. You may design a neural network to tell your whether or not there is a tumor in the image, but it is not a trivial task for a neural network to tell you where it is located.
If you do decide to let your network determine whether or not a given image contains a tumor, you would need a huge amount of images without tumors as well. The ratio of "images with tumor" and "images without tumor" should be close to the actual ratio observed in the real world. If you defere from this ratio, the network will be proned to false positives - as it learns that a majority of the images should contain tumors.
In your case
If you input a MR image which contains a tumor, and want to receive a segmented tumor image, you should probably have 500*500 input signals and 500*500 output signals - and train the network to create a border around the tumor present in the image.
If you extend you question as to explain why you want to make the neural network behave like this, then there might be someone here at SO that could help you!