By Edsger W. Dijkstra
He starts via contemplating the questions, «What is an algorithm?» and «What are we doing after we program?» those questions lead him to a fascinating digression at the semantics of programming languages, which, in flip, results in essays on programming language constructs, scoping of variables, and array references. Dijkstra then gives you, as promised, a set of lovely algorithms. those algorithms are a ways ranging, masking mathematical computations, different types of sorting difficulties, development matching, convex hulls, and extra. simply because this is often an outdated publication, the algorithms offered are often not the simplest on hand. notwithstanding, the price in examining A self-discipline of Programming is to take in and comprehend the way in which that Dijkstra considered those difficulties, which, in many ways, is extra worthy than 1000 algorithms.
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Extra resources for A Discipline of Programming
The matrix C can be computed from the first derivatives in a window around x, weighted by a Gaussian G(x, σ˜ ): C(x, σ, σ˜ ) = G(x, σ˜ ) Ix2 (x, σ ) Ix Iy (x, σ ) Ix Iy (x, σ ) Iy2 (x, σ ) . 3) 14 3. 2: The Harris detector searches for image neighborhoods where the second-moment matrix C has two large eigenvalues, corresponding to two dominant orientations. The resulting points often correspond to corner-like structures. Courtesy of Dennis Simakov and Darya Frolova. In this formulation, the convolution with the Gaussian G(x, σ˜ ) takes the role of summing over all pixels in a circular local neighborhood, where each pixel’s contribution is additionally weighted by its proximity to the center point.
2 Binary Embedding Functions Embedding functions are a related mechanism that are used to map expensive distance functions into something more manageable computationally. Either constructed or learned, these embeddings aim to approximately preserve the desired distance function when mapping to a low-dimensional space that is more easily searchable with known techniques. Informally, given an original feature space X and associated distance function dX , the basic idea is to designate a function f : X → E that maps the inputs into a new space E with associated distance dE in such a way that dE (f (x), f (y )) ≈ dX (x, y ), for any x, y ∈ X .
For each sampled location, the gradient orientation is entered into a coarser 4 × 4 grid of gradient orientation histograms with 8 orientation bins each, weighted by the corresponding pixel’s gradient magnitude and by a circular Gaussian weighting function with a σ of half the region size. The purpose of this Gaussian window is to give higher weights to pixels closer to the middle of the region, which are less affected by small localization inaccuracies of the interest region detector. 8. The motivation for this choice of representation is that the coarse spatial binning allows for small shifts due to registration errors without overly affecting the descriptor.