Graded convolutional networks improve image recognition under blur
Graded convolutional networks: scale invariance without the scale and robustness to unknown blur
Computer Vision and Pattern RecognitionMachine Learning
Summary
Images can be blurry or scaled differently, which makes it hard for computer programs to recognize what's in them. The authors developed a new way to process images using something called graded convolutional networks that handle different image sizes and unknown blurs better. Their method keeps much higher accuracy when recognizing digits even if the images are blurred. This approach helps the network focus on important features that don’t change with scale or blur.
What this means in practice
- •For computer vision engineers: Improve digit recognition systems to maintain accuracy under unknown blurring conditions using graded convolutional networks.
- •For autonomous vehicle developers: Enhance object detection algorithms to be robust against varying image blur caused by environmental factors.
Authors
Tanush Shaska
Abstract
The Gaussian jet of an image is a graded vector space: a dilation by $λ$ multiplies derivatives of order $k$ by $λ^{-k}$. Local graded convolutions are exactly homogeneous differential operators, and a local feature is dilation-invariant if and only if it factors through the scale-normalized jet or, without the scale, through the retraction onto the weighted sphere of the grading. Under unknown Gaussian blur the retraction changes only by a change of scale, whereas the scale-normalized jet acquires a grading factor that no radial normalization removes. At the zero jet the retraction separates image families that radial normalizations and continuous classifiers cannot. Networks built on the retraction are universal for invariant features. On MNIST such a network keeps 88.4% accuracy under a two-pixel blur, against 66.2% for the same network on scale-normalized derivatives; in Lindeberg's Gaussian derivative network the retraction raises accuracy at that blur from 91.5% to 95.1%.