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Computer Vision involves many challenging problems. While early work utilized classic methods, in recent years solutions have often relied on deep neural networks. In this study, we explore those two classes of methods through two applications that are at the limit of the ability of current computer vision algorithms, i.e., faint edge detection and multispectral image registration. We show that the detection of edges at a low signal-to-noise ratio is a demanding task with proven lower bounds. The introduced method processes straight and curved edges in nearly linear complexity. Moreover, performance is of high quality on noisy simulations, boundary datasets, and real images. However, in order to improve accuracy and runtime, a deep solution was also explored. It utilizes a multiscale neural network for the detection of edges in binary images using edge preservation loss. The second group of work that is considered in this study addresses multispectral image alignment. Since multispectral fusion is particularly informative, robust image alignment algorithms are required. However, as this cannot be carried out by single-channel registration methods, we propose a traditional approach that relies on a novel edge descriptor using a feature-based registration scheme. Experiments demonstrate that, although it is able to align a wide field of spectral channels, it lacks robustness to deal with every geometric transformation. To that end, we developed a deep approach for such alignment. Contrarily to the previously suggested edge descriptor, our deep approach uses an invariant representation for spectral patches via metric learning that can be seen as a teacher-student method. All those pieces of work are reported in five published papers with state-of-the-art experimental results and proven theory. As a whole, this research reveals that, while traditional methods are rooted in theoretical principles and are robust to a wide field of images, deep approaches are faster to run and achieve better performance if, not only sufficient training data are available, but also they are of the same image type as the data on which they are applied.