How to detect simple geometric shapes using OpenCV

You can also use template matching to detect shapes inside an image.

The answer depends on the presence of other shapes, level of noise if any and invariance you want to provide for (e.g. rotation, scaling, etc). These requirements will define not only the algorithm but also required pre-procesing stages to extract features.

Template matching that was suggested above works well when shapes aren't rotated or scaled and when there are no similar shapes around; in other words, it finds a best translation in the image where template is located:

double minVal, maxVal;
Point minLoc, maxLoc;
Mat image, template, result; // template is your shape
matchTemplate(image, template, result, CV_TM_CCOEFF_NORMED);
minMaxLoc(result, &minVal, &maxVal, &minLoc, &maxLoc); // maxLoc is answer

Geometric hashing is a good method to get invariance in terms of rotation and scaling; this method would require extraction of some contour points.

Generalized Hough transform can take care of invariance, noise and would have minimal pre-processing but it is a bit harder to implement than other methods. OpenCV has such transforms for lines and circles.

In the case when number of shapes is limited calculating moments or counting convex hull vertices may be the easiest solution: openCV structural analysis

If you have only these regular shapes, there is a simple procedure as follows :

1. Find Contours in the image ( image should be binary as given in your question)
2. Approximate each contour using approxPolyDP function.
3. First, check number of elements in the approximated contours of all the shapes. It is to recognize the shape. For eg, square will have 4, pentagon will have 5. Circles will have more, i don't know, so we find it. ( I got 16 for circle and 9 for half-circle.)
4. Now assign the color, run the code for your test image, check its number, fill it with corresponding colors.

Below is my example in Python:

import numpy as np
import cv2

img = cv2.imread('shapes.png')
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)

ret,thresh = cv2.threshold(gray,127,255,1)

contours,h = cv2.findContours(thresh,1,2)

for cnt in contours:
    approx = cv2.approxPolyDP(cnt,0.01*cv2.arcLength(cnt,True),True)
    print len(approx)
    if len(approx)==5:
        print "pentagon"
        cv2.drawContours(img,[cnt],0,255,-1)
    elif len(approx)==3:
        print "triangle"
        cv2.drawContours(img,[cnt],0,(0,255,0),-1)
    elif len(approx)==4:
        print "square"
        cv2.drawContours(img,[cnt],0,(0,0,255),-1)
    elif len(approx) == 9:
        print "half-circle"
        cv2.drawContours(img,[cnt],0,(255,255,0),-1)
    elif len(approx) > 15:
        print "circle"
        cv2.drawContours(img,[cnt],0,(0,255,255),-1)

cv2.imshow('img',img)
cv2.waitKey(0)
cv2.destroyAllWindows()

Below is the output:

Remember, it works only for regular shapes.

Alternatively to find circles, you can use houghcircles. You can find a tutorial here.

Regarding iOS, OpenCV devs are developing some iOS samples this summer, So visit their site : www.code.opencv.org and contact them.

You can find slides of their tutorial here : http://code.opencv.org/svn/gsoc2012/ios/trunk/doc/CVPR2012_OpenCV4IOS_Tutorial.pdf