Photoshop での磁気なげなわの大まかな実装 (Python ベース)

输入:
  s              // 种子点
  l(q,r)         // 计算局部cost

数据结构:
  L             // 当前待处理的像素
  N(q)          // 当前像素相邻的像素
  e(q)          // 标记一个像素是否已经做过相邻像素展开的Bool函数
  g(q)          // 从s到q的总cost

输出:
  p             // 记录所有路径的map

算法:
  g(s)←0; L←s;                 // 将种子点作为第一点初始化
  while L≠Ø:                   // 遍历尚未结束
    q←min(L);                  // 取出最小cost的像素并从待处理像素中移除
    e(q)←TRUE;                 // 将当前像素记录为已经做过相邻像素展开
    for each r∈N(q) and not e(r):
      gtemp←g(q)+l(q,r);        // 计算相邻像素的总cost
      if r∈L and gtemp<g(r):    // 找到了更好的路径
        r←L; { from list.}     // 舍弃较大cost的路径
      else if r∉L:
        g(r)←gtemp;             // 记录当前找到的最小路径
        p(r)←q;
        L←r;                    // 加入待处理以试图寻找更短的路径

from __future__ import division
import cv2
import numpy as np

SQRT_0_5 = 0.70710678118654757

class Livewire():
    """
    A simple livewire implementation for verification using 
        1. Canny edge detector + gradient magnitude + gradient direction
        2. Dijkstra algorithm
    """
    
    def __init__(self, image):
        self.image = image
        self.x_lim = image.shape[0]
        self.y_lim = image.shape[1]
        # The values in cost matrix ranges from 0~1
        self.cost_edges = 1 - cv2.Canny(image, 85, 170)/255.0
        self.grad_x, self.grad_y, self.grad_mag = self._get_grad(image)
        self.cost_grad_mag = 1 - self.grad_mag/np.max(self.grad_mag)
        # Weight for (Canny edges, gradient magnitude, gradient direction)
        self.weight = (0.425, 0.425, 0.15)
        
        self.n_pixs = self.x_lim * self.y_lim
        self.n_processed = 0
    
    @classmethod
    def _get_grad(cls, image):
        """
        Return the gradient magnitude of the image using Sobel operator
        """
        rgb = True if len(image.shape) > 2 else False
        grad_x = cv2.Sobel(image, cv2.CV_64F, 1, 0, ksize=3)
        grad_y = cv2.Sobel(image, cv2.CV_64F, 0, 1, ksize=3)
        if rgb:
            # A very rough approximation for quick verification...
            grad_x = np.max(grad_x, axis=2)
            grad_y = np.max(grad_y, axis=2)
            
        grad_mag = np.sqrt(grad_x**2+grad_y**2)
        grad_x /= grad_mag
        grad_y /= grad_mag
        
        return grad_x, grad_y, grad_mag
    
    def _get_neighbors(self, p):
        """
        Return 8 neighbors around the pixel p
        """
        x, y = p
        x0 = 0 if x == 0 else x - 1
        x1 = self.x_lim if x == self.x_lim - 1 else x + 2
        y0 = 0 if y == 0 else y - 1
        y1 = self.y_lim if y == self.y_lim - 1 else y + 2
        
        return [(x, y) for x in xrange(x0, x1) for y in xrange(y0, y1) if (x, y) != p]
    
    def _get_grad_direction_cost(self, p, q):
        """
        Calculate the gradient changes refer to the link direction
        """
        dp = (self.grad_y[p[0]][p[1]], -self.grad_x[p[0]][p[1]])
        dq = (self.grad_y[q[0]][q[1]], -self.grad_x[q[0]][q[1]])
        
        l = np.array([q[0]-p[0], q[1]-p[1]], np.float)
        if 0 not in l:
            l *= SQRT_0_5
        
        dp_l = np.dot(dp, l)
        l_dq = np.dot(l, dq)
        if dp_l < 0:
            dp_l = -dp_l
            l_dq = -l_dq
        
        # 2/3pi * ...
        return 0.212206590789 * (np.arccos(dp_l)+np.arccos(l_dq))
    
    def _local_cost(self, p, q):
        """
        1. Calculate the Canny edges & gradient magnitude cost taking into account Euclidean distance
        2. Combine with gradient direction
        Assumption: p & q are neighbors
        """
        diagnol = q[0] == p[0] or q[1] == p[1]
        
        # c0, c1 and c2 are costs from Canny operator, gradient magnitude and gradient direction respectively
        if diagnol:
            c0 = self.cost_edges[p[0]][p[1]]-SQRT_0_5*(self.cost_edges[p[0]][p[1]]-self.cost_edges[q[0]][q[1]])
            c1 = self.cost_grad_mag[p[0]][p[1]]-SQRT_0_5*(self.cost_grad_mag[p[0]][p[1]]-self.cost_grad_mag[q[0]][q[1]])
            c2 = SQRT_0_5 * self._get_grad_direction_cost(p, q)
        else:
            c0 = self.cost_edges[q[0]][q[1]]
            c1 = self.cost_grad_mag[q[0]][q[1]]
            c2 = self._get_grad_direction_cost(p, q)
        
        if np.isnan(c2):
            c2 = 0.0
        
        w0, w1, w2 = self.weight
        cost_pq = w0*c0 + w1*c1 + w2*c2
        
        return cost_pq * cost_pq

    def get_path_matrix(self, seed):
        """
        Get the back tracking matrix of the whole image from the cost matrix
        """
        neighbors = []          # 8 neighbors of the pixel being processed
        processed = set()       # Processed point
        cost = {seed: 0.0}      # Accumulated cost, initialized with seed to itself
        paths = {}

        self.n_processed = 0
        
        while cost:
            # Expand the minimum cost point
            p = min(cost, key=cost.get)
            neighbors = self._get_neighbors(p)
            processed.add(p)

            # Record accumulated costs and back tracking point for newly expanded points
            for q in [x for x in neighbors if x not in processed]:
                temp_cost = cost[p] + self._local_cost(p, q)
                if q in cost:
                    if temp_cost < cost[q]:
                        cost.pop(q)
                else:
                    cost[q] = temp_cost
                    processed.add(q)
                    paths[q] = p
            
            # Pop traversed points
            cost.pop(p)
            
            self.n_processed += 1
        
        return paths

livewire.py

 from __future__ import division
import time
import cv2
from PyQt4 import QtGui, QtCore
from threading import Thread
from livewire import Livewire

class ImageWin(QtGui.QWidget):
    def __init__(self):
        super(ImageWin, self).__init__()
        self.setupUi()
        self.active = False
        self.seed_enabled = True
        self.seed = None
        self.path_map = {}
        self.path = []
        
    def setupUi(self):
        self.hbox = QtGui.QVBoxLayout(self)
        
        # Load and initialize image
        self.image_path = ''
        while self.image_path == '':
            self.image_path = QtGui.QFileDialog.getOpenFileName(self, '', '', '(*.bmp *.jpg *.png)')
        self.image = QtGui.QPixmap(self.image_path)
        self.cv2_image = cv2.imread(str(self.image_path))
        self.lw = Livewire(self.cv2_image)
        self.w, self.h = self.image.width(), self.image.height()
        
        self.canvas = QtGui.QLabel(self)
        self.canvas.setMouseTracking(True)
        self.canvas.setPixmap(self.image)
        
        self.status_bar = QtGui.QStatusBar(self)
        self.status_bar.showMessage('Left click to set a seed')
        
        self.hbox.addWidget(self.canvas)
        self.hbox.addWidget(self.status_bar)
        self.setLayout(self.hbox)
    
    def mousePressEvent(self, event):            
        if self.seed_enabled:
            pos = event.pos()
            x, y = pos.x()-self.canvas.x(), pos.y()-self.canvas.y()
            
            if x < 0:
                x = 0
            if x >= self.w:
                x = self.w - 1
            if y < 0:
                y = 0
            if y >= self.h:
                y = self.h - 1

            # Get the mouse cursor position
            p = y, x
            seed = self.seed
            
            # Export bitmap
            if event.buttons() == QtCore.Qt.MidButton:
                filepath = QtGui.QFileDialog.getSaveFileName(self, &#39;Save image audio to&#39;, &#39;&#39;, &#39;*.bmp\n*.jpg\n*.png&#39;)
                image = self.image.copy()
                
                draw = QtGui.QPainter()
                draw.begin(image)
                draw.setPen(QtCore.Qt.blue)
                if self.path_map:
                    while p != seed:
                        draw.drawPoint(p[1], p[0])
                        for q in self.lw._get_neighbors(p):
                            draw.drawPoint(q[1], q[0])
                        p = self.path_map[p]
                if self.path:
                    draw.setPen(QtCore.Qt.green)
                    for p in self.path:
                        draw.drawPoint(p[1], p[0])
                        for q in self.lw._get_neighbors(p):
                            draw.drawPoint(q[1], q[0])
                draw.end()
                
                image.save(filepath, quality=100)
            
            else:
                self.seed = p
                
                if self.path_map:
                    while p != seed:
                        p = self.path_map[p]
                        self.path.append(p)
                
                # Calculate path map
                if event.buttons() == QtCore.Qt.LeftButton:
                    Thread(target=self._cal_path_matrix).start()
                    Thread(target=self._update_path_map_progress).start()
                
                # Finish current task and reset
                elif event.buttons() == QtCore.Qt.RightButton:
                    self.path_map = {}
                    self.status_bar.showMessage(&#39;Left click to set a seed&#39;)
                    self.active = False
    
    def mouseMoveEvent(self, event):
        if self.active and event.buttons() == QtCore.Qt.NoButton:
            pos = event.pos()
            x, y = pos.x()-self.canvas.x(), pos.y()-self.canvas.y()

            if x < 0 or x >= self.w or y < 0 or y >= self.h:
                pass
            else:
                # Draw livewire
                p = y, x
                path = []
                while p != self.seed:
                    p = self.path_map[p]
                    path.append(p)
                
                image = self.image.copy()
                draw = QtGui.QPainter()
                draw.begin(image)
                draw.setPen(QtCore.Qt.blue)
                for p in path:
                    draw.drawPoint(p[1], p[0])
                if self.path:
                    draw.setPen(QtCore.Qt.green)
                    for p in self.path:
                        draw.drawPoint(p[1], p[0])
                draw.end()
                self.canvas.setPixmap(image)
    
    def _cal_path_matrix(self):
        self.seed_enabled = False
        self.active = False
        self.status_bar.showMessage(&#39;Calculating path map...&#39;)
        path_matrix = self.lw.get_path_matrix(self.seed)
        self.status_bar.showMessage(r&#39;Left: new seed / Right: finish&#39;)
        self.seed_enabled = True
        self.active = True
        
        self.path_map = path_matrix
    
    def _update_path_map_progress(self):
        while not self.seed_enabled:
            time.sleep(0.1)
            message = &#39;Calculating path map... {:.1f}%&#39;.format(self.lw.n_processed/self.lw.n_pixs*100.0)
            self.status_bar.showMessage(message)
        self.status_bar.showMessage(r&#39;Left: new seed / Right: finish&#39;)

gui.py

import sys
from PyQt4 import QtGui
from gui import ImageWin

def main():
    app = QtGui.QApplication(sys.argv)
    window = ImageWin()
    window.setMouseTracking(True)
    window.setWindowTitle('Livewire Demo')
    window.show()
    window.setFixedSize(window.size())
    sys.exit(app.exec_())

if __name__ == '__main__':
    main()    

main.py