[SOLVED] How to search for the position of specific XY pairs in a 2 dimensional numpy array?

Issue

I have an image stored as 3 Numpy arrays:

# Int arrays of coordinates
# Not continuous, some points are omitted
X_image = np.array([1,2,3,4,5,6,7,9])
Y_image = np.array([9,8,7,6,5,4,3,1])

# Float array of RGB values.
# Same index
rgb = np.array([
    [0.5543,0.2665,0.5589],
    [0.5544,0.1665,0.5589],
    [0.2241,0.6645,0.5249],
    [0.2242,0.6445,0.2239],
    [0.2877,0.6425,0.5829],
    [0.5543,0.3165,0.2839],
    [0.3224,0.4635,0.5879],
    [0.5534,0.6693,0.5889],
])

The RGB information is not convertible to int. So it has to stay floats

I have another array that defines the position of an area of some pixels in the image:

X_area = np.array([3,4,6])
Y_area = np.array([7,6,4])

I need to find the RGB information for these pixels, using the first 4 arrays as a reference.

My idea was to search for the index of these area points in the full image and then use this index to find back the RGB information.

index = search_for_index_of_array_1_in_array_2((X_area,Y_area),(X_image,Y_image))

# index shall be [3,4,6]
rgb_area = rgb[index]

The search_for_index_of_array_1_in_array_2 can be implemented with a for loop. I tried it, this is too slow. I actually have millions of points.

I know that it is probably more of a use case for Julia than Python, as we deal with low-level data manipulation with a performance need, but I’m obliged to use Python. So, the only performance trick I see is to use a vectorized solution with NumPy.

I’m not used to manipulating NumPy. I tried numpy.where.

index = np.where(X_area in X_image and Y_area in Y_image )
index

Gives :

<ipython-input-18-0e434ab7a291>:1: DeprecationWarning: elementwise comparison failed; this will raise an error in the future.
  index = np.where(X_area in X_image and Y_area in Y_image )
(array([], dtype=int64),)

It shall be empty as we have 3 compliant points.

I also tested, with the same result:

XY_image = np.vstack((X_image,Y_image))
XY_area = np.vstack((X_area,Y_area))
index = np.where(XY_area == XY_image)

and even:

np.extract(XY_image == XY_area, XY_image)

If I get it, the issue is that the arrays do not have the same length. But this is what I have.

Do you have an idea of how to proceed?

Thanks

Edit: here is a loop that works but… is not fast:

indexes = []
for i in range(XY_area.shape[1]):
    XY_area_b =  np.broadcast_to(XY_area[:,i],(9,2)).transpose()
    where_in_image = np.where(XY_area_b == XY_image)
    index_in_image = where_in_image[1][1]
    indexes.append(index_in_image)
indexes

Solution

The classical method to solve this problem is generally to use a hashmap. However, Numpy do not provide such a data structure. That being said, an alternative (generally slower) solution is to sort the values and then perform a binary search. Hopefully, Numpy provide useful functions to do that. This solution run in O(n log(m)) (with n the number of value to search and m the number of value searched) should be much faster than a linear search running in O(n m) time. Here is an example:

# Format the inputs
valType = X_image.dtype
assert Y_image.dtype == valType and X_area.dtype == valType and X_image.dtype == valType
pointType = [('x', valType),('y', valType)]
XY_image = np.ravel(np.column_stack((X_image, Y_image))).view(pointType)
XY_area = np.ravel(np.column_stack((X_area, Y_area))).view(pointType)

# Build an index to sort XY_image and then generate the sorted points
sortingIndex = np.argsort(XY_image)
sorted_XY_image = XY_image[sortingIndex]

# Search each value of XY_area in XY_image and find the location in the unsorted array
tmp = np.searchsorted(XY_image, XY_area)
index = sortingIndex[tmp]

rgb_area = rgb[index]

Answered By – Jérôme Richard

Answer Checked By – Terry (BugsFixing Volunteer)

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