Is it feasible to train a Machine Learning Model (with image inputs) in an average personal computer? There are lots of examples of machine learning systems that can recognize objects and extract other information from images with very high precision. To train the models of such systems is necessary (I guess) a computer with a lot of computational power. 

My question is: For a system with images as inputs, depending on the complexity of the problem, is feasible to train a model in an average laptop? It will take to much time?

I know the time taken to train any machine learning model will be a function of lots of variables. I really don't expect a quantitative answer here, I just want to know whether I will be forced to upgrade my computer to develop and train machine learning models that have images as inputs.
You may play around on an average laptop but training will be very slow and you will be limited on the size of your model.
Once you try to build something more serious you will run out of memory very fast. A system with a GPU is recommended if you want to really do things like image recognition. If you buy something I would not go for any GPU with less than 8 GB memory and for an X99 motherboard to keep the flexibility to add a second GPU on full speed later if needed.
Don't mix up image recognition running on phones etc. Those are trained models and actually just being applied that is much easier process. Training is way much more expensive.