![]() In particular, we assume that both $h_i$ (with $i=1,2$) are sequences of $n\in\mathbb$. For simplicity, we consider two one-dimensional, single channel images, say $h_1$ and $h_2$, of the same size. Simple Histograms and Naive Distanceīefore we discuss the earth mover’s distance, let’s define the objects we will be interested in comparing. Interestingly, a similarity measure that works fairly well for image comparison is the so called earth mover’s distance. If we take the moon s current rate of recession and project it back in time, we end up with a collision. A choice of a distance metric is appropriate if it adequately reflects our perception of similarity for the given objects. These have shown that the moon is currently moving 3.8 cm away from the Earth every year. For specific objects, various functions could play the role of a distance metric, so long as they are symmetric, non-negative and satisfy the triangle-inequality as described in the link above. A different approach that may be somewhat less powerful, but works consistently on any set of examples, is the introduction of a mathematical distance metric. There is also no guarantee that the trained model will generalize well to all previously unseen examples. This approach requires an elaborate machine training process and large amounts of training data. Here x has m2 masses and y has n3 masses. An example pair of distributions in R2 is shown below. ![]() Nowadays, sophisticated techniques exist to accomplish this task, e.g., making use of neural networks and cleverly designed machine learning architectures. The Earth Mover's Distance (EMD) is a distance measure between discrete, finite distributions The x distribution has an amount of mass or weight w i at position x i in RK, i1.,m, while the y distribution has weight u j at position y j, j1.,n. ![]() Oftentimes we are interested in programmatically answering the question: how similar are two given objects of some kind, a prime example being the degree of similarity between two images. ![]()
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