Python scipy.numpy.convolve和scipy.signal.fft包含不同的结果

Question

我有2个阵列(G和G_).它们具有相同的形状和大小,我想对它们进行卷积.我找到了numpy.convolve和fftconvolve.我的代码就像:

foldedX = getFoldGradientsFFT(G, G_)
foldedY = getFoldGradientsNumpy(G, G_)

def getFoldGradientsFFT(G, G_):
    # convolve via scipy fast fourier transform  
    X =signal.fftconvolve(G,G_, "same)
    X*=255.0/numpy.max(X);
    return X

def getFoldGradientsNumpy(G, G_):
    # convolve via numpy.convolve
    Y = ndimage.convolve(G, G_)
    Y*=255.0/numpy.max(Y);
    return Y

但结果却不尽相同.结果如:Numpy.concolve()

[  11.60287582    3.28262652   18.80395211   52.75829556   99.61675945 
147.74124258  187.66178244  215.06160439  234.1907606   229.04221552]

scipy.signal.fftconvolve:

[ -4.88130620e-15   6.74371119e-02   4.91875539e+00   1.94250997e+01
3.88227012e+01   6.70322921e+01   9.78460423e+01   1.08486302e+02
1.17267015e+02   1.15691562e+02]

我认为结果应该是相同的,即使这两个函数用不同的程序进行卷积？!

---

我忘了提一下,我想要卷积2个二维数组:S数组:

G = array([[1,2],[3,4]])
G_ = array([[5,6],[7,8]])

代码

def getFoldGradientsFFT(G, G_):
    X =signal.fftconvolve(G,G_,"same")
    X=X.astype("int")
    X*=255.0/np.max(X);
    return X

def getFoldGradientsNumpy(G, G_):
    # convolve via convolve
    old_shape = G.shape
    G = np.reshape(G, G.size)
    G_ = np.reshape(G_, G.size)
    Y = np.convolve(G, G_, "same")
    Y = np.reshape(Y,old_shape)
    Y = Y.astype("int")
    Y*=255.0/np.max(Y);
    return Y

def getFoldGradientsNDImage(G, G_):
    Y = ndimage.convolve(G, G_)
    Y = Y.astype("int")
    Y *= 255.0/np.max(Y)
    return Y

结果:

getFoldGradientsFFT
[[ 21  68]
[ 93 255]]

getFoldGradientsNumpy
[[ 66 142]
[250 255]]

getFoldGradientsNDImage
[[147 181]
[220 255]]

Answer 1

numpy.convolve用于一维数据.

以下代码比较signal.convolve,signal.fftconvolve和ndimage.convolve的结果.

对于ndimage.convolve,我们需要将mode参数设置为"constant",当N为偶数时,将origin参数设置为-1,当N为奇数时,将参数设置为0.

from scipy import signal
from scipy import ndimage
import numpy as np

np.random.seed(1)

for N in xrange(2, 20):
    a = np.random.randint(0, 10, size=(N, N))
    b = np.random.randint(0, 10, size=(N, N))

    r1 = signal.convolve(a, b, mode="same")
    r2 = signal.fftconvolve(a, b, mode="same")
    r3 = ndimage.convolve(a, b, mode="constant", origin=-1 if N%2==0 else 0)
    print "N=", N
    print np.allclose(r1, r2)
    print np.allclose(r2, r3)