  Current research in Computer Vision has shown that Convolutional Neural
Networks (CNN) give state-of-the-art performance in many classification tasks
and Computer Vision problems. The embedding of CNN, which is the internal
representation produced by the last layer, can indirectly learn topological and
relational properties. Moreover, by using a suitable loss function, CNN models
can learn invariance to a wide range of non-linear distortions such as
rotation, viewpoint angle or lighting condition. In this work, new insights are
discovered about CNN embeddings and a new loss function is proposed, derived
from the contrastive loss, that creates models with more predicable mappings
and also quantifies distortions. In typical distortion-dependent methods, there
is no simple relation between the features corresponding to one image and the
features of this image distorted. Therefore, these methods require to
feed-forward inputs under every distortions in order to find the corresponding
features representations. Our contribution makes a step towards embeddings
where features of distorted inputs are related and can be derived from each
others by the intensity of the distortion.
