# tangent distance between two handwritten digits

Suppose we have two handwritten images "3"MNIST three and "6"MNIST six. The task is to compute the tangent distance between the two. An explanation at undergraduate level is highly appreciated.

• What do you know about the topic so far? Do you know the definition of tangent distance? – Matti P. Jan 22 at 10:38
• Here is something about the topic : cedar.buffalo.edu/~srihari/CSE555/… – Matti P. Jan 22 at 10:41
• great slides. thank you. Suppose, we consider only rotation. Then the tangent vector $TV$ correspondes to the difference between the image $x'$ (as colomn vector) rotated $\alpha$ degrees around the center and the unrotated image (also as column vector) i.e., $$\mathrm{\boldsymbol{TV}} = \mathcal{F}(\boldsymbol{x}^\prime; \alpha) - \boldsymbol{x}'$$ (see slide 38). Is this correct? Do I have to compute the tangent vector for any rotation angle $\alpha$ ? – Alexander K. Jan 22 at 15:09