SEMINAR by Sophie Langer (University of Twente)

December 02, 2022

11:00

Louvain-la-Neuve

ISBA - C115 (1st Floor)

Statistics Seminar on "Image classification: A (new) statistical viewpoint"

Abstract :
In this talk we consider a simple supervised classification problem for object recognition on grayscale images. There are two possible perspectives to solve this problem. Firstly, one can interpret object recognition as a high-dimensional classification problem, where every pixel is a variable. The task is then to map these pixel values to the conditional class probabilities or the labels. Increasing the dimension makes the problem considerably harder, leading to slow convergence rates due to the curse of dimensionality. Another perspective is to view images as two-dimensional objects. Increasing the number of pixels leads to higher resolution and therefore better performance is expected for large images. Following the second route, we present a new image deformation model, for which we propose and analyze two different classifiers. The first method estimates the image deformation by support alignment. Under a minimal separation condition, it is shown that perfect classification is possible. The second method fits a CNN to the data. We derive a rate for the misclassification error depending on the sample size and the number of pixels $d^2$. Under suitable conditions, this rate is of order $1/\sqrt{d}.$ Because of the setting we have chosen, not only are our methods not affected by the curse of high dimension, but they actually improve with increasing dimension.

Categories Events: