# The Joint Manifold Model

### Ram Navaratnam, Andrew Fitzgibbon, Roberto Cipolla

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## Abstract

Many computer vision tasks may be expressed as the problem of learning a
mapping between image space and a parameter space. For example, in human
body pose estimation, recent research has directly modelled the mapping
from image features (*z*) to joint angles (θ). Fitting such models
requires training data in the form of labelled (*z*,θ) pairs, from
which are learned the conditional densities p(θ | *z*). Inference is
then simple: given test image features *z*, the conditional p(θ |
*z*) is immediately computed. However large amounts of training data are
required to fit the models, particularly in the case where the spaces are
high dimensional.
We show how the use of * unlabelled * data&emdash;samples from
the marginal distributions p(*z*) and p(θ)&em;may be used to improve
fitting. This is valuable because it is often
significantly easier to obtain unlabelled than labelled samples.
We use a Gaussian
process latent variable model to learn the mapping from a shared
latent low-dimensional manifold to the feature and parameter spaces. This
extends existing approaches to (a) use unlabelled data, and (b) represent
one-to-many mappings.

Experiments on synthetic and real problems demonstrate how the use of
unlabelled data improves over existing techniques. In our comparisons, we
include existing approaches that are explicitly semi-supervised as well
as those which implicitly make use of unlabelled examples.

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