在 MatplotLib 3D 散点图中绘制边界框

Question

I'd like to draw a bounding box around my 3D Scatterplot datapoints without having to resort to Microsoft Paint. Is there an easy way to do this in MatplotLib?

Answer 1

You need to define where your vertices are, and which edges need connecting. Assuming you have defined a set of edges as pairs of vertices in some list AllEdgesVertexPairs , ask matplotlib to make a line for each pair.

#Plot a line segment for each edge pair:
for SingleEdgeVertexPair in AllEdgesVertexPairs:
    Vertex1 = SingleEdgeVertexPair[0]
    Vertex2 = SingleEdgeVertexPair[1]

    EdgeXvals = [Vertex1[0], Vertex2[0] ]
    EdgeYvals = [Vertex1[1], Vertex2[1] ]
    EdgeZvals = [Vertex1[2], Vertex2[2] ]

    matplotlib.pyplot.plot(
        EdgeXvals, 
        EdgeYvals,
        EdgeZvals,  
        c='k', 
        marker=None,
        linestyle = '-',
        linewidth = 0.2,
        )

In a particular case for myself, I needed to plot a cube so my AllEdgesVertexPairs looked like:

[[[ 16.  16. 115.]
  [-14.  16. 115.]]
 [[ 16.  16. 115.]
  [ 16. -14. 115.]]
 [[ 16.  16. 115.]
  [ 16.  16.  85.]]
 [[-14.  16. 115.]
  [-14. -14. 115.]]
 [[-14.  16. 115.]
  [-14.  16.  85.]]
 [[ 16. -14. 115.]
  [-14. -14. 115.]]
 [[ 16. -14. 115.]
  [ 16. -14.  85.]]
 [[-14. -14. 115.]
  [-14. -14.  85.]]
 [[ 16.  16.  85.]
  [-14.  16.  85.]]
 [[ 16.  16.  85.]
  [ 16. -14.  85.]]
 [[-14.  16.  85.]
  [-14. -14.  85.]]
 [[ 16. -14.  85.]
  [-14. -14.  85.]]]

In your case you will also need 8 vertices, and 12 edges. However, its not super obvious how you will choose them.

If you need an algorithm to choose the bounding vertices yourself based on your image, I would suggest the following:

• Calculate principle components from eigenvalues / eigenvectors of a covariance matrix.
• Use a rectangular prism centered upon the mean of your data
• side lengths = 2*StdDev on each principle axis
• Use the eigenvectors to find the vertex locations from the mean

By doing it with PCA and rectangular prism, you can make a mathematical statement about how many points will be inside your "bounding box". (you are basically approximating an ellipsoid derived from a multivariate Gaussian with a rectangular box). There are likely better or more clever algorithms out there.