I'm working on a program that lets the user draw a digit in a "scribbling area" and with the press of a button the application will predict the digit that he entered, using a neural net classifier.
Now, to train the neural net, I used MNIST database which specifies the following: "images from NIST were size normalized to fit in a 20x20 pixel box while preserving their aspect ratio [...] the images were centered in a 28 x 28 image by computing the center of mass of the pixels".
The problem that I'm facing is that after resizing the digit that the user drew in the scribbling area to a size of 20 x 20, I need to compute the center of mass of the pixels so I can center it in the middle of the 28 x 28 image.
How can I compute that ?
"Center of mass" (for binary images) is a bit convoluted way of saying "mean value across each dimension". In other words - take all x coordinates and average them - and you got x coordinate of your "center of mass", the same for y.
In python, for data in X it would be
center_of_mass = X.mean(axis=0)
If you have pixels' intensities you can use them as "weights" thus leading to weighted averages, that's all.
Here, let me search that for you ...
You multiply the distance from the mean by the weight of each pixel -- almost certainly 1.0 for your work. In short, take the mean of all x coordinates and the mean of all y coordinates; that gives you the center of mass.
来源：https://stackoverflow.com/questions/37448873/center-of-mass-of-pixels-in-grayscale-image