  Inspired by CapsNet's routing-by-agreement mechanism with its ability to
learn object properties, we explore if those properties in turn can determine
new properties of the objects, such as the locations. We then propose a CapsNet
architecture with object coordinate atoms and a modified routing-by-agreement
algorithm with unevenly distributed initial routing probabilities. The model is
based on CapsNet but uses a routing algorithm to find the objects' approximate
positions in the image coordinate system. We also discussed how to derive the
property of translation through coordinate atoms and we show the importance of
sparse representation. We train our model on the single moving MNIST dataset
with class labels. Our model can learn and derive the coordinates of the digits
better than its convolution counterpart that lacks a routing-by-agreement
algorithm, and can also perform well when testing on the multi-digit moving
MNIST and KTH datasets. The results show our method reaches the state-of-art
performance on object localization without any extra localization techniques
and modules as in prior work.
