Fundamentals of digital image processing
Fundamentals of digital image processing
Group theoretical methods in image processing
Group theoretical methods in image processing
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
On Learning Vector-Valued Functions
Neural Computation
Invariance in kernel methods by haar-integration kernels
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
The Journal of Machine Learning Research
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This paper presents a new class of matrix valued kernels that are ideally suited to learn vector valued equivariant functions. Matrix valued kernels are a natural generalization of the common notion of a kernel. We set the theoretical foundations of so called equivariant matrix valued kernels. We work out several properties of equivariant kernels, we give an interpretation of their behavior and show relations to scalar kernels. The notion of (ir)reducibility of group representations is transferred into the framework of matrix valued kernels. At the end to two exemplary applications are demonstrated. We design a non-linear rotation and translation equivariant filter for 2D-images and propose an invariant object detector based on the generalized Hough transform.