分形信息维度和相关维度

Question

我的任务是计算给定图像（分形）的分形维数。具体来说，我想计算信息的维度和相关性的维度（Grassberger，1983 年；Grassberger 和 Procaccia，1983 年）。我无法创建自己的实现，除了 this 之外，我找不到任何实现。我试图将它从 C++ 转换为 python，但我得到了意想不到的值（比如错误的值或负维度！）。

这是我的代码（仅用于信息维度——我还没有为相关维度编写代码）：

def information_dimension(image, lmax=64, step=2):
    """
    Calculates the information dimension of the given image.

    Parameters:
    image (ndarray): 2D array representing the image
    lmax (int): maximum box size for calculation
    step (int): factor by which to increase the box size

    Returns:
    float: information dimension of the image
    """
    print("Calculating Information Dimension:")

    # get image dimensions
    height, width, dummy = np.shape(image)
    print(f"Selection w: {width}, h: {height}")


    # calculate new width and height without edge pixels
    wn = int((width // lmax) * lmax)
    hn = int((height // lmax) * lmax)
    print(f"Calculating over w={wn} and h={hn}")

    # calculate logarithm of total number of pixels
    loghw = np.log(hn * wn)

    # initialize variables
    fractdim = 0
    boxes = []
    nboxes = []
    boxsize = 2

    # loop over increasing box sizes
    while boxsize <= lmax:
        inf = 0
        te = 0
        freq = boxsize * boxsize

        # loop over boxes
        for k in range(0, hn - boxsize + 1, boxsize):
            for l in range(0, wn - boxsize + 1, boxsize):
                # find minimum and maximum pixel values in box
                box = image[k:k+boxsize, l:l+boxsize]
                box_min = np.amin(box)
                box_max = np.amax(box)

                # calculate number of boxes needed to cover range of pixel values
                n = (box_max - box_min) // boxsize + 1
                te += int(n) 

                # calculate relative frequency of box and add to information sum
                inf += freq * (np.log(freq / n) - loghw)

        # calculate information dimension for current box size
        print(f"(N: {te}) ", end="")
        inf = inf / (hn * wn)
        print(f"inf={inf:.6f} for boxsize {boxsize}")
        boxes.append(np.log(boxsize))
        nboxes.append(inf)

        # increase box size
        boxsize *= step

    # calculate slope of regression line to obtain fractal dimension
    coeffs = np.polyfit(boxes, nboxes, 1)
    fractdim = coeffs[0]
    print(f"\nSlope (Fract. Dim) is {fractdim:.6f} with correlation {np.corrcoef(boxes, nboxes)[0, 1]:.6f}")

    return fractdim