#### Title of Poster / Presentation

#### Start Date

10-5-2017 11:00 AM

#### End Date

10-5-2017 1:00 PM

#### Subjects

Image processing -- Digital techniques, Stochastic processes -- Mathematical models, Poisson processes

#### Abstract

We present a model that utilizes Cox processes and CNN classifiers in order to count the number of instances of an object in an image. Poisson processes are well suited to events that occur randomly in space, like the location of objects in an image, as well as to the task of counting. Mixed Poisson processes also offer increased flexibility, however they do not easily scale with image size: they typically require O(n3) computation time and O(n2) storage, where n is the number of pixels. To mitigate this problem, we employ Kronecker algebra which takes advantage of the direct product structure of the covariance matrix. As the likelihood is non Gaussian, we use Laplace Approximation for inference, which involves using the conjugate gradient and Newton’s method. Our approach has close to linear performance, requiring only O(n3/2) computation time and O(n) memory. In practice, we select a subset of bounding boxes in the image and we query them for the presence of the object by running a pre-trained CNN classifier like AlexNet. We aggregate the observations and compute a posterior distribution, which is then used to estimate the number of instances of the object in the entire image. We show results on both simulated data and on images from MS COCO dataset. We also compare our counting results with Faster RCNN, and show that for the task of counting, we out-perform or match the RCNN.

#### Persistent Identifier

http://archives.pdx.edu/ds/psu/20022

Cox Processes for Visual Object Counting

We present a model that utilizes Cox processes and CNN classifiers in order to count the number of instances of an object in an image. Poisson processes are well suited to events that occur randomly in space, like the location of objects in an image, as well as to the task of counting. Mixed Poisson processes also offer increased flexibility, however they do not easily scale with image size: they typically require O(n3) computation time and O(n2) storage, where n is the number of pixels. To mitigate this problem, we employ Kronecker algebra which takes advantage of the direct product structure of the covariance matrix. As the likelihood is non Gaussian, we use Laplace Approximation for inference, which involves using the conjugate gradient and Newton’s method. Our approach has close to linear performance, requiring only O(n3/2) computation time and O(n) memory. In practice, we select a subset of bounding boxes in the image and we query them for the presence of the object by running a pre-trained CNN classifier like AlexNet. We aggregate the observations and compute a posterior distribution, which is then used to estimate the number of instances of the object in the entire image. We show results on both simulated data and on images from MS COCO dataset. We also compare our counting results with Faster RCNN, and show that for the task of counting, we out-perform or match the RCNN.