def gen_dgauss(sigma):
'''
gradient of the gaussian on both directions.
'''
fwid = np.int(2 * np.ceil(sigma))
G = np.array(range(-fwid, fwid + 1)) ** 2
G = G.reshape((G.size, 1)) + G
G = np.exp(- G / 2.0 / sigma / sigma)
G /= np.sum(G)
GH, GW = np.gradient(G)
GH *= 2.0 / np.sum(np.abs(GH))
GW *= 2.0 / np.sum(np.abs(GW))
return GH, GW
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