  Click-based interactive segmentation (IS) aims to extract the target objects
under user interaction. For this task, most of the current deep learning
(DL)-based methods mainly follow the general pipelines of semantic
segmentation. Albeit achieving promising performance, they do not fully and
explicitly utilize and propagate the click information, inevitably leading to
unsatisfactory segmentation results, even at clicked points. Against this
issue, in this paper, we propose to formulate the IS task as a Gaussian process
(GP)-based pixel-wise binary classification model on each image. To solve this
model, we utilize amortized variational inference to approximate the
intractable GP posterior in a data-driven manner and then decouple the
approximated GP posterior into double space forms for efficient sampling with
linear complexity. Then, we correspondingly construct a GP classification
framework, named GPCIS, which is integrated with the deep kernel learning
mechanism for more flexibility. The main specificities of the proposed GPCIS
lie in: 1) Under the explicit guidance of the derived GP posterior, the
information contained in clicks can be finely propagated to the entire image
and then boost the segmentation; 2) The accuracy of predictions at clicks has
good theoretical support. These merits of GPCIS as well as its good generality
and high efficiency are substantiated by comprehensive experiments on several
benchmarks, as compared with representative methods both quantitatively and
qualitatively.
