Hi 又见面啦！

不知道小伙伴们最近有没有好好学习软件呢

今天我将带领大家从【测量篇】开始学习，要学习到的算法就是——最小外接矩形！

机器视觉定位方法很多如：

基于特征点匹配的、基于形状的、基于外截圆、外截矩形的等等。其中基于最小外接矩形的定位方法是我们常见的一种定位方法。

其定位机理可以概述为：通过查找目标特征区域的最小外接矩形，依据矩形的位置及方向来定位目标物体的位置与姿态。再通过与模板图像的比对，从而计算出目标物体的偏移量与旋转角度，从而引导机械手进行相应的作业。

✔算法介绍

本算法用于统计在设定的 ROI 区域（蓝色框）内统计符合灰度要求的像素点组成的最小单位的矩形，设定区域面积的【合格范围】，从而判断产品OK/NG.

✔参数学习

【灰度低阈值】：设置值应<=检测位置边缘灰度值，确定检测位置需要被检测到的像素点灰度的最小值；

【灰度高阈值】：设置值应>=检测位置边缘灰度值，确定检测位置需要被检测到的像素点灰度的最大值；

【精度放大倍数】：此值越高计算出的结果值越精确，但同时会增加检测时间，

【最小阈值】：设置值应<=测试结果值，确定合格产品范围的最小值；

【最大阈值】：设置值应>=测试结果值，确定合格产品范围的最大值；

【收缩检测区域】：此功能可一键自动调整 ROI 区域大小范围（可多次调整），其中“膨胀尺寸”和“向外扩展”可设置单次向外扩展的大小

最小外接矩形算法实际应用场景 ：检测物体(如玻璃瓶的瓶口高度)是否有半圆缺失等...

我们先打开SGVision软件，按【F4】快捷键进入算法页面，【导入需要检测的图片】—【选择测量栏目】—【选中最小外接矩形】。

假设我们要寻找这张图片

也就是白色区域的最小外

他的【RGB】是255，所以灰度最高最低阈值只要在这个范围就可以检测出来！

，时长00:21

检测一下

它就自动寻找出最小的外接矩形了

这个时候我们测出来的参数有长和宽，有最小宽度和最大宽度，那我们根据客户的要求看他是想要提取哪个参数。

我们再来换一个不同形状的来测试一下！

圆形的最小外接矩形

测试一下也很快就找到了最小的外接矩形

，时长00:09

那假设我们想要找的是最外面这个圆的最小外接矩形，那我们要怎么把里面的圆过滤掉从而精准的找到呢，答案就是调整参数。

我们把【灰度低阈值】与【灰度高阈值】调整为:

80—150

测试一下就找到了！

，时长00:13

所以大家在寻找最小外接矩形的时候要先确认好阈值范围，以免碰到多层图形的时候找错图形。

最小外接矩形呢比较适合不规则图形去寻找它的最小的长和宽，如果是圆形这样的图形精度就没那么准确了，总的来说这个算法相对简单，也没有那么多复杂的参数，非常好上手的！

完整视频教学：

https://mp.weixin.qq.com/s/TMGQs5uOgzca0yIjv9Re4whttps://mp.weixin.qq.com/s/TMGQs5uOgzca0yIjv9Re4w

说明：

在MATLAB中常常会用到对识别分割出来的物体进行最小外接矩形的处理，进而在原图中显示分割结果
这里常用的函数minboundrect.m

function [rectx,recty,area,perimeter] = minboundrect(x,y,metric)
% minboundrect: Compute the minimal bounding rectangle of points in the plane
% usage: [rectx,recty,area,perimeter] = minboundrect(x,y,metric)
%
% arguments: (input)
%  x,y - vectors of points, describing points in the plane as
%        (x,y) pairs. x and y must be the same lengths.
%
%  metric - (OPTIONAL) - single letter character flag which
%        denotes the use of minimal area or perimeter as the
%        metric to be minimized. metric may be either 'a' or 'p',
%        capitalization is ignored. Any other contraction of 'area'
%        or 'perimeter' is also accepted.
%
%        DEFAULT: 'a'    ('area')
%
% arguments: (output)
%  rectx,recty - 5x1 vectors of points that define the minimal
%        bounding rectangle.
%
%  area - (scalar) area of the minimal rect itself.
%
%  perimeter - (scalar) perimeter of the minimal rect as found
%
%
% Note: For those individuals who would prefer the rect with minimum
% perimeter or area, careful testing convinces me that the minimum area
% rect was generally also the minimum perimeter rect on most problems
% (with one class of exceptions). This same testing appeared to verify my
% assumption that the minimum area rect must always contain at least
% one edge of the convex hull. The exception I refer to above is for
% problems when the convex hull is composed of only a few points,
% most likely exactly 3. Here one may see differences between the
% two metrics. My thanks to Roger Stafford for pointing out this
% class of counter-examples.
%
% Thanks are also due to Roger for pointing out a proof that the
% bounding rect must always contain an edge of the convex hull, in
% both the minimal perimeter and area cases.
%
%
% See also: minboundcircle, minboundtri, minboundsphere
%
%
% default for metric
if (nargin<3) || isempty(metric)
  metric = 'a';
elseif ~ischar(metric)
  error 'metric must be a character flag if it is supplied.'
else
  % check for 'a' or 'p'
  metric = lower(metric(:)');                    
  ind = strmatch(metric,{'area','perimeter'});             
  if isempty(ind)                
    error 'metric does not match either ''area'' or ''perimeter'''
  end

  % just keep the first letter.
  metric = metric(1);
end

% preprocess data
x=x(:);
y=y(:);

% not many error checks to worry about
n = length(x);                                    
if n~=length(y)                               
  error 'x and y must be the same sizes'
end

% start out with the convex hull of the points to
% reduce the problem dramatically. Note that any
% points in the interior of the convex hull are
% never needed, so we drop them.
if n>3
%   edges = convhull(x,y,{'Qt'});  % 'Pp' will silence the warnings
edges = convhull(x,y);
  % exclude those points inside the hull as not relevant
  % also sorts the points into their convex hull as a
  % closed polygon

  x = x(edges);
  y = y(edges);

  % probably fewer points now, unless the points are fully convex
  nedges = length(x) - 1;                       
elseif n>1
  % n must be 2 or 3
  nedges = n;
  x(end+1) = x(1);
  y(end+1) = y(1);
else
  % n must be 0 or 1
  nedges = n;
end

% now we must find the bounding rectangle of those
% that remain.

% special case small numbers of points. If we trip any
% of these cases, then we are done, so return.
switch nedges
  case 0
    % empty begets empty
    rectx = [];
    recty = [];
    area = [];
    perimeter = [];
    return
  case 1
    % with one point, the rect is simple.
    rectx = repmat(x,1,5);
    recty = repmat(y,1,5);
    area = 0;
    perimeter = 0;
    return
  case 2
    % only two points. also simple.
    rectx = x([1 2 2 1 1]);
    recty = y([1 2 2 1 1]);
    area = 0;
    perimeter = 2*sqrt(diff(x).^2 + diff(y).^2);
    return
end
% 3 or more points.

% will need a 2x2 rotation matrix through an angle theta
Rmat = @(theta) [cos(theta) sin(theta);-sin(theta) cos(theta)];

% get the angle of each edge of the hull polygon.
ind = 1:(length(x)-1);
edgeangles = atan2(y(ind+1) - y(ind),x(ind+1) - x(ind));
% move the angle into the first quadrant.
edgeangles = unique(mod(edgeangles,pi/2));

% now just check each edge of the hull
nang = length(edgeangles);              
area = inf;                           
perimeter = inf;
met = inf;
xy = [x,y];
for i = 1:nang                         
  % rotate the data through -theta 
  rot = Rmat(-edgeangles(i));
  xyr = xy*rot;
  xymin = min(xyr,[],1);
  xymax = max(xyr,[],1);

  % The area is simple, as is the perimeter
  A_i = prod(xymax - xymin);
  P_i = 2*sum(xymax-xymin);

  if metric=='a'
    M_i = A_i;
  else
    M_i = P_i;
  end

  % new metric value for the current interval. Is it better?
  if M_i<met
    % keep this one
    met = M_i;
    area = A_i;
    perimeter = P_i;

    rect = [xymin;[xymax(1),xymin(2)];xymax;[xymin(1),xymax(2)];xymin];
    rect = rect*rot';
    rectx = rect(:,1);
    recty = rect(:,2);
  end
end
% get the final rect

% all done

end % mainline end

测试文件：

close all;
clc;
I=imread('2.jpg');
bw=im2bw(I);
[labelpic,num]=bwlabel(bw,8);
[r c]=find(labelpic==1);
[rectx,recty,area,perimeter]=minboundrect(c,r,'p'); %%'a'是按最小面积算，如果按边长算，用'p'
imshow(bw);
hold on
line(rectx(:),recty(:),'color','g'); 

[r c]=find(labelpic==2);
[rectx,recty,area,perimeter]=minboundrect(c,r,'p');
line(rectx(:),recty(:),'color','r');  

[r c]=find(labelpic==3);
[rectx,recty,area,perimeter]=minboundrect(c,r,'p');
line(rectx(:),recty(:),'color','r');