Demonstration of OpenCV's cv2 API for manipulating images, creating contours, simplifying those contours and creating various bounding structures.  I started with Abid Rahman's Contours 1 and 2 blog posts.  Those posts do not directly give you all that you need to run them.  By virtue of being an IPython Notebook, these are the actual command that worked for me.  You will need wget, numpy, matplotlib, OpenCV and shapely.

-kurt schwehr 2013-Jan-31
# BEGIN http://www.opencvpython.blogspot.com/2012/06/hi-this-article-is-tutorial-which-try.html

!wget http://3.bp.blogspot.com/-a5blM3JLkIU/T9OXg1YhN0I/AAAAAAAAASQ/MbdfSG2oaYg/s200/test.jpg

import numpy as np
import cv2
import cv
import shapely.geometry

im = cv2.imread('test.jpg')

whos

imgray = cv2.cvtColor(im, cv2.COLOR_BGR2GRAY)

ret, thresh = cv2.threshold(imgray, 127, 255, 0)
imshow(thresh)

contours, hierarchy = cv2.findContours(thresh, cv2.RETR_TREE, cv2.CHAIN_APPROX_SIMPLE)
imshow(thresh)

len(contours), hierarchy

len(contours[0])

cv2.drawContours(im, contours, -1, (0,255,0), 3)
imshow(im)

cv2.drawContours(im, contours, -1, (0,255,0), -1)
imshow(im)

cv2.drawContours(im, contours, 0, (0,255,0), 1)
imshow(im)

!wget http://3.bp.blogspot.com/-1UtLXb7c73U/T9QZT3tpVjI/AAAAAAAAATE/Nyo7SFg8T1o/s1600/balls.png

im = cv2.imread('balls.png')
imgray = cv2.cvtColor(im, cv2.COLOR_BGR2GRAY)

ret, thresh = cv2.threshold(imgray, 100, 255, 0)
imshow(thresh)

contours, hierarchy = cv2.findContours(thresh, cv2.RETR_TREE, cv2.CHAIN_APPROX_SIMPLE)

for h, cnt in enumerate(contours):
    mask = np.zeros(imgray.shape, np.uint8)
    cv2.drawContours(mask, [cnt], 0, 255, -1)
    mean = cv2.mean(im, mask=mask)
    print h, mean

# END http://www.opencvpython.blogspot.com/2012/06/hi-this-article-is-tutorial-which-try.html

moments = cv2.moments(contours[0])
area = moments['m00']
moments

cv2.contourArea(contours[0])

perimeter = cv2.arcLength(contours[0], True) # True says that curve is closed
perimeter

cnt = contours[0]
len(cnt)

x = cnt[:,0, 0]; y = cnt[:,0,1]
plot(x,y)


simpler = cv2.approxPolyDP(cnt, 2, True)
plot(simpler[:,0,0], simpler[:,0,1])

hull = cv2.convexHull(cnt)
plot(hull[:,0,0], hull[:,0,1])

simpler_hull = cv2.approxPolyDP(hull, 2.5, True)
plot(simpler_hull[:,0,0], simpler_hull[:,0,1])
plot(x,y)

r_x, r_y, r_w, r_h = cv2.boundingRect(cnt)
r_x, r_y, r_w, r_h  # (150, 121, 103, 146)
plot((r_x, r_x, r_x+r_w, r_x+r_w, r_x), (r_y, r_y+r_h, r_y+r_h, r_y, r_y))
plot(x,y)

rect = cv2.minAreaRect(cnt)
rect # ((202.134521484375, 192.14178466796875), (102.39618682861328, 140.3079376220703), -5.128190994262695)
box = cv2.cv.BoxPoints(rect)
box # ((157.41201782226562, 266.59124755859375), (144.87069702148438, 126.84494018554688), (246.85702514648438, 117.69232177734375), (259.3983459472656, 257.4386291503906))
# plot( [p[0] for p in box] + [box[0][0]], [p[1] for p in box] + [box[0][1]] )
box_list = list(box)
box_list.append(box[0])
ba = np.array(box_list) # Box array
plot(ba[:,0], ba[:,1])
plot(x,y)

(c_x, c_y), radius = cv2.minEnclosingCircle(cnt)
c_x, c_y, radius # (197.0, 194.5, 82.92139434814453)
center = shapely.geometry.Point(c_x, c_y)
circle = np.array(center.buffer(radius).boundary.coords)
len(circle) # 66 points
plot(circle[:,0], circle[:,1])
plot(x,y)

ellipse = cv2.fitEllipse(cnt)
ellipse # ((199.31251525878906, 185.9192352294922), (93.7149658203125, 138.58531188964844), 202.948486328125)
# TODO: what is a convenient way to get the coords for an ellipse?