Can translational invariance of CNNs be unwanted if object is likely in certain positions? Various texts on using CNNs for object detection in images talk about how their translation invariance is a good thing. Which makes sense for tasks where the object could be anywhere in the image. Let's say detecting a kitten in household images.

But let's say, you already have some information about the likely position of the object of interest in the image. For example, for detecting trees in a dataset of images of landscapes. Here in most cases, the trees are going to be in the bottom half of the image while in some cases they might be at the top (because it's on a hill or whatever). So you want your neural network to learn that information -- that trees are likely connected to the bottom part of the image (ground). Is this possible using the CNN paradigm? 

Thank you
According to your example:

Trees will likely be in the bottom half of the image. Still, you will not know whether there will be one, two or five trees. Thanks to translation invariance property of CNN's, each tree will activate filters responsible for tree detection. You still need to handle those few exceptions where trees are on hill.

To achieve better results in this particular case, you might want to consider some kind of focus mechanism, that will try to get rid of unwanted part of picture, in case when there are (for example) no hills. Take a look at Spatial Transformer Networks. During training it learns to predict spatial transformation (for example zoom) that will help "main" classifier to predict class of image.