SIFT算法之关键点查找

SIFT算法之关键点查找

1. 综述

利用SIFT算法找到输入图像的关键点，预期效果如下图所示。

2. 基本实现

    2.1 读入图像并利用PIL.ImageOps.grayscale() 函数转换成灰度图，除以255以normalize到[0,1]范围内。

    2.2 利用scipy函数scipy.ndimage.gaussian_laplace(input, sigma, output=None, mode='reflect', cval=0.0, **kwargs) 来对图像进行gaussian Laplacian 算子卷积。(函数参数解读见附录1)。 注意此处需要进行scale normalize的操作，对结果乘以sigma*2（可以求平方得到squared laplacian response in scale space. 求平方是为了将白点和黑点统一化）

          设置不同的一系列不同的sigma值分别对图像进行卷积。得到一个三维的矩阵，第三个维度为sigma

    (由于gaussian Laplacian算子不可以通过分解来降维，所以当sigma变大的时候卷积速度会大幅度下降，所以可以采用skimage.transform.resize(matrix, size = (newx,newy))的方法对图像进行不同程度的降采样然后用同一个gaussian Laplacian算子卷积后再upsample到原来的大小，这个方法可以大幅度提升卷积速度)

     2.3 对这个三维的scale space进行nonmaximum suppress，找到矩阵的三维极大值。输出(x,y, 1.414 * sigma)作为圆心坐标（可能会用到IOU，没有实现）

      2.4 画图,利用如下函数

def show_all_circles(image, circles, color='r'):
    """
    image: numpy array, representing the grayscsale image
    cx, cy: numpy arrays or lists, centers of the detected blobs
    rad: numpy array or list, radius of the detected blobs
    """
    import matplotlib.pyplot as plt
    from matplotlib.patches import Circle

    fig, ax = plt.subplots()
    ax.set_aspect('equal')
    ax.imshow(image, cmap='gray')
    for circle in circles:
        circ = Circle((circle[1], circle[0]), circle[2], color=color, fill=False)
        ax.add_patch(circ)

    plt.title('%i circles' % len(circles))
    plt.show()
    return 0

3. 实验结果

4. Difference of Gaussian

    In David G. Lowe’s paper, Difference of Gaussian can be viewed as an approximationof the Gaussian Laplace filter. The formula is given as follows:

            G(x,y,kσ)-G(x,y,σ)≈(k-1)σ^2 ∇^2 G

    TheLHS of the above equation is the original scale-invariant Gaussian Laplacianresponse and the RHS is the difference of two gaussian responses.

     What we have to do is to downsample theimage from the original size to several levels and a Gaussian filter with samesigma is applied to each level of image. Rescale every downsampled responsematrix to the original image size and stack each matrix and finally get a 3D arrayand the shape of which is [level, x, y]. Get (levels -1) differences between eachpair of adjacent layers. The rest work of nonmaximum suppression is similar toLaplacian Gaussian method.

    （以上英文段落引自本人实验报告）

附录

1. filter函数参数解读

scipy.ndimage.gaussian_laplace(input, sigma, output=None, mode='reflect', cval=0.0, **kwargs)

Parameters:

input : array_like Input array to filter. sigma : scalar or sequence of scalars The standard deviations of the Gaussian filter are given for each axis as a sequence, or as a single number, in which case it is equal for all axes. output : array, optional The output parameter passes an array in which to store the filter output. Output array should have different name as compared to input array to avoid aliasing errors. mode : str or sequence, optional The mode parameter determines how the array borders are handled. Valid modes are {‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’}. cval is the value used when mode is equal to ‘constant’. A list of modes with length equal to the number of axes can be provided to specify different modes for different axes. Default is ‘reflect’ cval : scalar, optional Value to fill past edges of input if mode is ‘constant’. Default is 0.0 Extra keyword arguments will be passed to gaussian_filter().

2. 如何由函数gaussian_filter的truncate 和 sigma参数确定filter的宽度？

以下引自 Stack Overflow https://stackoverflow.com/questions/25216382/gaussian-filter-in-scip

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Check out the source code here: https://github.com/scipy/scipy/blob/master/scipy/ndimage/filters.py

You'll see that gaussian_filter calls gaussian_filter1d for each axis. In gaussian_filter1d, the width of the filter is determined implicitly by the values of sigma and truncate. In effect, the width w is

w = 2*int(truncate*sigma + 0.5) + 1

So

(w