<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def outline(labels):
 """Given a label matrix, return a matrix of the outlines of the labeled objects If a pixel is not zero and has at least one neighbor with a different value, then it is part of the outline. """

    
    output = numpy.zeros(labels.shape, labels.dtype)
    lr_different = labels[1:,:]!=labels[:-1,:]
    ud_different = labels[:,1:]!=labels[:,:-1]
    d1_different = labels[1:,1:]!=labels[:-1,:-1]
    d2_different = labels[1:,:-1]!=labels[:-1,1:]
    different = numpy.zeros(labels.shape, bool)
    different[1:,:][lr_different]  = True
    different[:-1,:][lr_different] = True
    different[:,1:][ud_different]  = True
    different[:,:-1][ud_different] = True
    different[1:,1:][d1_different] = True
    different[:-1,:-1][d1_different] = True
    different[1:,:-1][d2_different] = True
    different[:-1,1:][d2_different] = True
    #
    # Labels on edges need outlines
    #
    different[0,:] = True
    different[:,0] = True
    different[-1,:] = True
    different[:,-1] = True
    
    output[different] = labels[different]
    return output