Using Principal Component Analysis for corner feature extraction
Neural networks can cope with not linearly separable classes, but they're not magic either. They still assume smooth decision boundaries, and I don't think your data would have those. 

And before you try to feed the same data to an SVM, RVM, random forest, or any other classifier: I don't think the corner coordinates are good features for any off-the-shelf classification algorithm. The typical input vector in machine learning is something like {age,weight,height,eye color}, where for every input vector, index 2 means "weight". In your input vector, index 2 can sometimes be a corner somewhere near the front wheel of the car, and in another case it's a corner near the roof. 

Have you tried simpler shape descriptors, like Fourier descriptors or maybe Hu moments?