如何去除凸面缺陷?

How to crop away convexity defects?

我正在尝试从轮廓中检测和精确定位图像中的某些对象。我得到的轮廓经常包含一些噪音(可能形成背景,我不知道)。这些对象应该看起来类似于矩形或正方形,例如:

我通过形状匹配 (cv::matchShapes) 获得了很好的结果来检测其中包含这些对象的轮廓,有无噪音,但我在噪音情况下的精确定位方面存在问题。

噪音看起来像:

例如

or

我的想法是找到凸面缺陷,如果它们变得太强,就以某种方式剪掉导致凹面的部分。检测缺陷是可以的,通常每个 "unwanted structure" 我会得到两个缺陷,但我仍然不知道如何决定我应该从轮廓中删除什么以及在哪里删除点。

这里有一些轮廓,它们的掩码(所以你可以很容易地提取轮廓)和包含阈值凸缺陷的凸包:

我可以只走遍等高线并在本地决定是否由等高线执行 "left turn"(如果顺时针走),如果是,则删除等高线点直到下一个左转弯?也许从凸缺陷开始?

我要找算法或者代码,编程语言应该不重要,算法更重要。

作为起点并假设缺陷相对于您要识别的对象永远不会太大,您可以在使用 cv::matchShapes 之前尝试简单的侵蚀+扩张策略,如下所示。

 int max = 40; // depending on expected object and defect size
 cv::Mat img = cv::imread("example.png");
 cv::Mat eroded, dilated;
 cv::Mat element = cv::getStructuringElement(cv::MORPH_ELLIPSE, cv::Size(max*2,max*2), cv::Point(max,max));
 cv::erode(img, eroded, element);
 cv::dilate(eroded, dilated, element);
 cv::imshow("original", img);
 cv::imshow("eroded", eroded);
 cv::imshow("dilated", dilated);

我想出了以下方法来检测 rectangle/square 的边界。它的工作基于几个假设:形状是矩形或正方形,它在图像中居中,不倾斜。

  • masked(filled) 图像沿着 x 轴分成两半,这样你就得到两个区域(上半部分和下半部分)
  • 将每个区域在 x 轴上的投影
  • 取这些预测的所有非零条目并取它们的中位数。这些中位数为您提供 y 范围
  • 类似地,将图像沿y轴分成两半,将投影投影到y轴,然后计算中位数以获得x边界
  • 使用边界裁剪区域

样本图像上半部分的中线和投影如下所示。

两个样本的边界和裁剪区域:

代码在Octave/Matlab,我在Octave上测试过(需要镜像包到运行)。

clear all
close all

im = double(imread('kTouF.png'));
[r, c] = size(im);
% top half
p = sum(im(1:int32(end/2), :), 1);
y1 = -median(p(find(p > 0))) + int32(r/2);
% bottom half
p = sum(im(int32(end/2):end, :), 1);
y2 = median(p(find(p > 0))) + int32(r/2);
% left half
p = sum(im(:, 1:int32(end/2)), 2);
x1 = -median(p(find(p > 0))) + int32(c/2);
% right half
p = sum(im(:, int32(end/2):end), 2);
x2 = median(p(find(p > 0))) + int32(c/2);

% crop the image using the bounds
rect = [x1 y1 x2-x1 y2-y1];
cr = imcrop(im, rect);
im2 = zeros(size(im));
im2(y1:y2, x1:x2) = cr;

figure,
axis equal
subplot(1, 2, 1)
imagesc(im)
hold on
plot([x1 x2 x2 x1 x1], [y1 y1 y2 y2 y1], 'g-')
hold off
subplot(1, 2, 2)
imagesc(im2)

这种方法只适用于点。您不需要为此创建掩码。

主要思想是:

  1. 在轮廓上查找缺陷
  2. 如果我找到至少两个缺陷,找到两个最接近的缺陷
  3. 从轮廓中移除两个最近缺陷之间的点
  4. 在新的轮廓上从 1 重新开始

我得到以下结果。如您所见,它对于 smooth 缺陷(例如第 7 张图像)有一些缺点,但对于清晰可见的缺陷非常有效。我不知道这是否能解决您的问题,但可以作为一个起点。实际上应该相当快(你当然可以优化下面的代码,特别是 removeFromContour 函数)。此外,这种方法的唯一参数是凸缺陷的数量,因此它适用于小缺陷斑点和大缺陷斑点。

#include <opencv2/opencv.hpp>
using namespace cv;
using namespace std;

int ed2(const Point& lhs, const Point& rhs)
{
    return (lhs.x - rhs.x)*(lhs.x - rhs.x) + (lhs.y - rhs.y)*(lhs.y - rhs.y);
}

vector<Point> removeFromContour(const vector<Point>& contour, const vector<int>& defectsIdx)
{
    int minDist = INT_MAX;
    int startIdx;
    int endIdx;

    // Find nearest defects
    for (int i = 0; i < defectsIdx.size(); ++i)
    {
        for (int j = i + 1; j < defectsIdx.size(); ++j)
        {
            float dist = ed2(contour[defectsIdx[i]], contour[defectsIdx[j]]);
            if (minDist > dist)
            {
                minDist = dist;
                startIdx = defectsIdx[i];
                endIdx = defectsIdx[j];
            }
        }
    }

    // Check if intervals are swapped
    if (startIdx <= endIdx)
    {
        int len1 = endIdx - startIdx;
        int len2 = contour.size() - endIdx + startIdx;
        if (len2 < len1)
        {
            swap(startIdx, endIdx);
        }
    }
    else
    {
        int len1 = startIdx - endIdx;
        int len2 = contour.size() - startIdx + endIdx;
        if (len1 < len2)
        {
            swap(startIdx, endIdx);
        }
    }

    // Remove unwanted points
    vector<Point> out;
    if (startIdx <= endIdx)
    {
        out.insert(out.end(), contour.begin(), contour.begin() + startIdx);
        out.insert(out.end(), contour.begin() + endIdx, contour.end());
    } 
    else
    {
        out.insert(out.end(), contour.begin() + endIdx, contour.begin() + startIdx);
    }

    return out;
}

int main()
{
    Mat1b img = imread("path_to_mask", IMREAD_GRAYSCALE);

    Mat3b out;
    cvtColor(img, out, COLOR_GRAY2BGR);

    vector<vector<Point>> contours;
    findContours(img.clone(), contours, RETR_EXTERNAL, CHAIN_APPROX_NONE);

    vector<Point> pts = contours[0];

    vector<int> hullIdx;
    convexHull(pts, hullIdx, false);

    vector<Vec4i> defects;
    convexityDefects(pts, hullIdx, defects);

    while (true)
    {
        // For debug
        Mat3b dbg;
        cvtColor(img, dbg, COLOR_GRAY2BGR);

        vector<vector<Point>> tmp = {pts};
        drawContours(dbg, tmp, 0, Scalar(255, 127, 0));

        vector<int> defectsIdx;
        for (const Vec4i& v : defects)
        {
            float depth = float(v[3]) / 256.f;
            if (depth > 2) //  filter defects by depth
            {
                // Defect found
                defectsIdx.push_back(v[2]);

                int startidx = v[0]; Point ptStart(pts[startidx]);
                int endidx = v[1]; Point ptEnd(pts[endidx]);
                int faridx = v[2]; Point ptFar(pts[faridx]);

                line(dbg, ptStart, ptEnd, Scalar(255, 0, 0), 1);
                line(dbg, ptStart, ptFar, Scalar(0, 255, 0), 1);
                line(dbg, ptEnd, ptFar, Scalar(0, 0, 255), 1);
                circle(dbg, ptFar, 4, Scalar(127, 127, 255), 2);
            }
        }

        if (defectsIdx.size() < 2)
        {
            break;
        }

        // If I have more than two defects, remove the points between the two nearest defects
        pts = removeFromContour(pts, defectsIdx);
        convexHull(pts, hullIdx, false);
        convexityDefects(pts, hullIdx, defects);
    }


    // Draw result contour
    vector<vector<Point>> tmp = { pts };
    drawContours(out, tmp, 0, Scalar(0, 0, 255), 1);

    imshow("Result", out);
    waitKey();

    return 0;
}

更新

在近似轮廓上工作(例如在 findContours 中使用 CHAIN_APPROX_SIMPLE)可能会更快,但必须使用 arcLength().

计算轮廓的长度

这是要在 removeFromContourswapping 部分替换的代码段:

// Check if intervals are swapped
if (startIdx <= endIdx)
{
    //int len11 = endIdx - startIdx;
    vector<Point> inside(contour.begin() + startIdx, contour.begin() + endIdx);
    int len1 = (inside.empty()) ? 0 : arcLength(inside, false);

    //int len22 = contour.size() - endIdx + startIdx;
    vector<Point> outside1(contour.begin(), contour.begin() + startIdx);
    vector<Point> outside2(contour.begin() + endIdx, contour.end());
    int len2 = (outside1.empty() ? 0 : arcLength(outside1, false)) + (outside2.empty() ? 0 : arcLength(outside2, false));

    if (len2 < len1)
    {
        swap(startIdx, endIdx);
    }
}
else
{
    //int len1 = startIdx - endIdx;
    vector<Point> inside(contour.begin() + endIdx, contour.begin() + startIdx);
    int len1 = (inside.empty()) ? 0 : arcLength(inside, false);


    //int len2 = contour.size() - startIdx + endIdx;
    vector<Point> outside1(contour.begin(), contour.begin() + endIdx);
    vector<Point> outside2(contour.begin() + startIdx, contour.end());
    int len2 = (outside1.empty() ? 0 : arcLength(outside1, false)) + (outside2.empty() ? 0 : arcLength(outside2, false));

    if (len1 < len2)
    {
        swap(startIdx, endIdx);
    }
}

这里是 Python 遵循 Miki 代码的实现。

import numpy as np
import cv2

def ed2(lhs, rhs):
    return(lhs[0] - rhs[0])*(lhs[0] - rhs[0]) + (lhs[1] - rhs[1])*(lhs[1] - rhs[1])


def remove_from_contour(contour, defectsIdx, tmp):
    minDist = sys.maxsize
    startIdx, endIdx = 0, 0

    for i in range(0,len(defectsIdx)):
        for j in range(i+1, len(defectsIdx)):
            dist = ed2(contour[defectsIdx[i]][0], contour[defectsIdx[j]][0])
            if minDist > dist:
                minDist = dist
                startIdx = defectsIdx[i]
                endIdx = defectsIdx[j]

    if startIdx <= endIdx:
        inside = contour[startIdx:endIdx]
        len1 = 0 if inside.size == 0 else cv2.arcLength(inside, False)
        outside1 = contour[0:startIdx]
        outside2 = contour[endIdx:len(contour)]
        len2 = (0 if outside1.size == 0 else cv2.arcLength(outside1, False)) + (0 if outside2.size == 0 else cv2.arcLength(outside2, False))
        if len2 < len1:
            startIdx,endIdx = endIdx,startIdx     
    else:
        inside = contour[endIdx:startIdx]
        len1 = 0 if inside.size == 0 else cv2.arcLength(inside, False)
        outside1 = contour[0:endIdx]
        outside2 = contour[startIdx:len(contour)]
        len2 = (0 if outside1.size == 0 else cv2.arcLength(outside1, False)) + (0 if outside2.size == 0 else cv2.arcLength(outside2, False))
        if len1 < len2:
            startIdx,endIdx = endIdx,startIdx

    if startIdx <= endIdx:
        out = np.concatenate((contour[0:startIdx], contour[endIdx:len(contour)]), axis=0)
    else:
        out = contour[endIdx:startIdx]
    return out


def remove_defects(mask, debug=False):
    tmp = mask.copy()
    mask = cv2.cvtColor(mask, cv2.COLOR_BGR2GRAY)

    # get contour
    contours, _ = cv2.findContours(
        mask, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_NONE)
    assert len(contours) > 0, "No contours found"
    contour = sorted(contours, key=cv2.contourArea)[-1] #largest contour
    if debug:
        init = cv2.drawContours(tmp.copy(), [contour], 0, (255, 0, 255), 1, cv2.LINE_AA)
        figure, ax = plt.subplots(1)
        ax.imshow(init)
        ax.set_title("Initital Contour")

    hull = cv2.convexHull(contour, returnPoints=False)
    defects = cv2.convexityDefects(contour, hull)

    while True:
        defectsIdx = []
        
        for i in range(defects.shape[0]):
            s, e, f, d = defects[i, 0]
            start = tuple(contour[s][0])
            end = tuple(contour[e][0])
            far = tuple(contour[f][0])
            
            depth = d / 256
            if depth > 2:
                defectsIdx.append(f)

        if len(defectsIdx) < 2:
            break

        contour = remove_from_contour(contour, defectsIdx, tmp)
        hull = cv2.convexHull(contour, returnPoints=False)
        defects = cv2.convexityDefects(contour, hull)

    if debug:
      rslt = cv2.drawContours(tmp.copy(), [contour], 0, (0, 255, 255), 1)
      figure, ax = plt.subplots(1)
      ax.imshow(rslt)
      ax.set_title("Corrected Contour")

mask = cv2.imread("a.png")
remove_defects(mask, True)