只是想告诉你们，有一个很好的选项可以用python在图像中找到局部最大值:

from skimage.feature import peak_local_max

或者对于skimage 0.8.0:

from skimage.feature.peak import peak_local_max

http://scikit-image.org/docs/0.8.0/api/skimage.feature.peak.html

如果你一步一步地进行:你首先找到全局最大值，如果需要处理周围的点，然后将找到的区域设置为零，然后对下一个重复。

我不确定这是否回答了问题，但似乎你可以只寻找n个没有邻居的最高的山峰。

这是要点。注意，它是用Ruby编写的，但其思想应该很清楚。

require 'pp'

NUM_PEAKS = 5
NEIGHBOR_DISTANCE = 1

data = [[1,2,3,4,5],
        [2,6,4,4,6],
        [3,6,7,4,3],
       ]

def tuples(matrix)
  tuples = []
  matrix.each_with_index { |row, ri|
    row.each_with_index { |value, ci|
      tuples << [value, ri, ci]
    }
  }
  tuples
end

def neighbor?(t1, t2, distance = 1)
  [1,2].each { |axis|
    return false if (t1[axis] - t2[axis]).abs > distance
  }
  true
end

# convert the matrix into a sorted list of tuples (value, row, col), highest peaks first
sorted = tuples(data).sort_by { |tuple| tuple.first }.reverse

# the list of peaks that don't have neighbors
non_neighboring_peaks = []

sorted.each { |candidate|
  # always take the highest peak
  if non_neighboring_peaks.empty?
    non_neighboring_peaks << candidate
    puts "took the first peak: #{candidate}"
  else
    # check that this candidate doesn't have any accepted neighbors
    is_ok = true
    non_neighboring_peaks.each { |accepted|
      if neighbor?(candidate, accepted, NEIGHBOR_DISTANCE)
        is_ok = false
        break
      end
    }
    if is_ok
      non_neighboring_peaks << candidate
      puts "took #{candidate}"
    else
      puts "denied #{candidate}"
    end
  end
}

pp non_neighboring_peaks

物理学家的解决办法: 定义5个爪标记，用它们的位置X_i来标识，并用随机的位置初始化它们。 定义一个能量函数，结合标记物在爪子位置的定位奖励和标记物重叠惩罚;比方说:

E(X_i;S)=-Sum_i(S(X_i))+alfa*Sum_ij (|X_i-Xj|<=2*sqrt(2)?1:0)

(S(X_i)是围绕X_i的2x2平方的平均力，阿尔法是一个实验峰值参数)

Now time to do some Metropolis-Hastings magic: 1. Select random marker and move it by one pixel in random direction. 2. Calculate dE, the difference of energy this move caused. 3. Get an uniform random number from 0-1 and call it r. 4. If dE<0 or exp(-beta*dE)>r, accept the move and go to 1; if not, undo the move and go to 1. This should be repeated until the markers will converge to paws. Beta controls the scanning to optimizing tradeoff, so it should be also optimized experimentally; it can be also constantly increased with the time of simulation (simulated annealing).

我用局部最大滤波器检测了峰值。下面是你的第一个4个爪子数据集的结果:

我还在9个爪子的第二个数据集上运行了它，效果也很好。

你可以这样做:

import numpy as np
from scipy.ndimage.filters import maximum_filter
from scipy.ndimage.morphology import generate_binary_structure, binary_erosion
import matplotlib.pyplot as pp

#for some reason I had to reshape. Numpy ignored the shape header.
paws_data = np.loadtxt("paws.txt").reshape(4,11,14)

#getting a list of images
paws = [p.squeeze() for p in np.vsplit(paws_data,4)]


def detect_peaks(image):
    """
    Takes an image and detect the peaks usingthe local maximum filter.
    Returns a boolean mask of the peaks (i.e. 1 when
    the pixel's value is the neighborhood maximum, 0 otherwise)
    """

    # define an 8-connected neighborhood
    neighborhood = generate_binary_structure(2,2)

    #apply the local maximum filter; all pixel of maximal value 
    #in their neighborhood are set to 1
    local_max = maximum_filter(image, footprint=neighborhood)==image
    #local_max is a mask that contains the peaks we are 
    #looking for, but also the background.
    #In order to isolate the peaks we must remove the background from the mask.

    #we create the mask of the background
    background = (image==0)

    #a little technicality: we must erode the background in order to 
    #successfully subtract it form local_max, otherwise a line will 
    #appear along the background border (artifact of the local maximum filter)
    eroded_background = binary_erosion(background, structure=neighborhood, border_value=1)

    #we obtain the final mask, containing only peaks, 
    #by removing the background from the local_max mask (xor operation)
    detected_peaks = local_max ^ eroded_background

    return detected_peaks


#applying the detection and plotting results
for i, paw in enumerate(paws):
    detected_peaks = detect_peaks(paw)
    pp.subplot(4,2,(2*i+1))
    pp.imshow(paw)
    pp.subplot(4,2,(2*i+2) )
    pp.imshow(detected_peaks)

pp.show()

之后你所需要做的就是在蒙版上使用scipy. nmage .measurements.label来标记所有不同的对象。然后你就可以单独和他们玩了。

注意，该方法工作得很好，因为背景没有噪声。如果是的话，你会在背景中检测到一堆其他不想要的峰。另一个重要因素是社区的大小。如果峰值大小发生变化，您将需要调整它(应该保持大致成比例)。

谢谢你的原始数据。我在火车上，这是我到的最远的地方(我的站就要到了)。我用regexps按摩了你的txt文件，并将其放入一个html页面，使用一些javascript进行可视化。我在这里分享它是因为一些人，比如我自己，可能会发现它比python更容易被破解。

我认为一个很好的方法是尺度和旋转不变，我的下一步将是研究高斯的混合。(每个爪垫是高斯分布的中心)。

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