(1) Abstract: We investigate the problem of image alignment by directly using pixel intensity values. This is a difficult nonconvex optimization task that is susceptible to local minima. Coarse-to-fine scheme has become a standard for direct intensity-based alignment. It is believed that such coarse-to-fine scale sampling (Gaussian blur) can improve region of attraction of the alignment optimization towards the global minimum. Nevertheless, it has been questioned whether such isotropic blur (Gaussian kernel) is indeed the universally optimal choice any arbitrary geometric transformation. Although some heuristic choices of non-Gaussian or anisotropic kernels have been proposed in the literature, no rigorously derived kernel for such tasks has been known to date. In this work, we derive optimal kernels for some of the common motion models such as affine and homography. These kernels are optimal in the sense of smoothing the optimization's objective function. This is useful, as such smoothing can eliminate small fluctuations and weak local minima in the objective. Our derivation shows that these kernels coincide with Gaussian blur of the image only for displacement motion. (2) Biography: Hossein Mobahi is a PhD student in University of Illinois at Urbana Champaign advised by Yi Ma. He has done works on Image Segmentation, 3D Reconstruction, and Face Recognition. His current research focuses on the role of smoothing in nonconvex optimization and its applications to computer vision problems. Throughout his graduate study, he has won several award including ACCV09 Best Student Paper award, Beckman's AI/Cognitive award for two years and Mavis Memorial Scholarship. He has been on UIUC's CSE fellowship since the past two years.