Question

我正在尝试使用优化技术而不是DLT（直接线性变换）方法来解决单应性（计算机视觉）问题。这个成本函数的简单说明如下： Illustration of cost function

我在python中实现了这个代价函数： -

def costFunc(H, p1, p2):
    cost = 0.
    H = H.reshape((3, 3))
    H_inv = inv(H)

    for i in range(0, p1.shape[0]):
        # Forward Transformation
        x = p1[i, :]
        x_dash = p2[i, :]

        x = numpy.reshape(x, [1, 3])
        x_dash_estimated = applyTransformation(H, x)

        diff = numpy.sum(numpy.square(numpy.subtract(x_dash_estimated, x_dash)))
        cost = cost + diff

        # # Inverse Transformation
        x = p2[i, :]
        x_dash = p1[i, :]

        x = numpy.reshape(x, [1, 3])
        x_dash_estimated = applyTransformation(H_inv, x)

        diff = numpy.sum(numpy.square(numpy.subtract(x_dash_estimated, x_dash)))
        cost = cost + diff
    return cost/p1.shape[0]

这里，H与给定图像的H矩阵（但是平展为1×9矢量）相同，并且p1和p2是4对应的均匀点。它们都是4x3矩阵。图像之间的对应点如下： -

refPt = numpy.array([[[182, 267, 1], [119, 270, 1]],
                     [[264, 111, 1], [202, 110, 1]],
                     [[544, 92, 1], [479, 95, 1]],
                     [[329, 356, 1], [269, 357, 1]]])

每行代表图像中的两个对应点。它们分为p1和p2： -

p1 = refPt[:, 0, :]
p2 = refPt[:, 1, :]

函数applyTransformation只是将单应性应用于输入点。它被命名为： -

def applyTransformation(H, points):
    output = numpy.zeros(shape=[points.shape[0], 3], dtype=numpy.int32)
    for i in range(0, points.shape[0]):
        temp = numpy.dot(H, points[i, :])
        temp = temp / temp[2]
        temp[0] = numpy.round(temp[0])
        temp[1] = numpy.round(temp[1])
        output[i, :] = temp

    return output

现在，当我尝试最小化此功能时，我陷入某些局部最小值并且永远不会实现全局最优值。我的优化代码如下： -

initial_H = numpy.random.rand(3, 3) * 1.
initial_h = initial_H.flatten()
result =  optimize.minimize(fun = costFunc,
                             x0 = initial_h,
                             args = (p1, p2),
                             method = 'TNC')

需要一些建议来解决这个问题。

Python函数没有优化

0 个答案: