  Image ordinal estimation is to predict the ordinal label of a given image,
which can be categorized as an ordinal regression problem. Recent methods
formulate an ordinal regression problem as a series of binary classification
problems. Such methods cannot ensure that the global ordinal relationship is
preserved since the relationships among different binary classifiers are
neglected. We propose a novel ordinal regression approach, termed Convolutional
Ordinal Regression Forest or CORF, for image ordinal estimation, which can
integrate ordinal regression and differentiable decision trees with a
convolutional neural network for obtaining precise and stable global ordinal
relationships. The advantages of the proposed CORF are twofold. First, instead
of learning a series of binary classifiers \emph{independently}, the proposed
method aims at learning an ordinal distribution for ordinal regression by
optimizing those binary classifiers \emph{simultaneously}. Second, the
differentiable decision trees in the proposed CORF can be trained together with
the ordinal distribution in an end-to-end manner. The effectiveness of the
proposed CORF is verified on two image ordinal estimation tasks, i.e. facial
age estimation and image aesthetic assessment, showing significant improvements
and better stability over the state-of-the-art ordinal regression methods.
