OpenCV
3.4.20dev
Open Source Computer Vision

Prev Tutorial: Contours : Getting Started
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Image moments help you to calculate some features like center of mass of the object, area of the object etc. Check out the wikipedia page on Image Moments
We use the function: cv.moments (array, binaryImage = false)
array  raster image (singlechannel, 8bit or floatingpoint 2D array) or an array ( 1×N or N×1 ) of 2D points. 
binaryImage  if it is true, all nonzero image pixels are treated as 1's. The parameter is used for images only. 
From this moments, you can extract useful data like area, centroid etc. Centroid is given by the relations, \(C_x = \frac{M_{10}}{M_{00}}\) and \(C_y = \frac{M_{01}}{M_{00}}\). This can be done as follows:
Contour area is given by the function cv.contourArea() or from moments, M['m00'].
We use the function: cv.contourArea (contour, oriented = false)
contour  input vector of 2D points (contour vertices) 
oriented  oriented area flag. If it is true, the function returns a signed area value, depending on the contour orientation (clockwise or counterclockwise). Using this feature you can determine orientation of a contour by taking the sign of an area. By default, the parameter is false, which means that the absolute value is returned. 
It is also called arc length. It can be found out using cv.arcLength() function.
We use the function: cv.arcLength (curve, closed)
curve  input vector of 2D points. 
closed  flag indicating whether the curve is closed or not. 
It approximates a contour shape to another shape with less number of vertices depending upon the precision we specify. It is an implementation of DouglasPeucker algorithm. Check the wikipedia page for algorithm and demonstration.
We use the function: cv.approxPolyDP (curve, approxCurve, epsilon, closed)
curve  input vector of 2D points stored in cv.Mat. 
approxCurve  result of the approximation. The type should match the type of the input curve. 
epsilon  parameter specifying the approximation accuracy. This is the maximum distance between the original curve and its approximation. 
closed  If true, the approximated curve is closed (its first and last vertices are connected). Otherwise, it is not closed. 
Convex Hull will look similar to contour approximation, but it is not (Both may provide same results in some cases). Here, cv.convexHull() function checks a curve for convexity defects and corrects it. Generally speaking, convex curves are the curves which are always bulged out, or atleast flat. And if it is bulged inside, it is called convexity defects. For example, check the below image of hand. Red line shows the convex hull of hand. The doublesided arrow marks shows the convexity defects, which are the local maximum deviations of hull from contours.
We use the function: cv.convexHull (points, hull, clockwise = false, returnPoints = true)
points  input 2D point set. 
hull  output convex hull. 
clockwise  orientation flag. If it is true, the output convex hull is oriented clockwise. Otherwise, it is oriented counterclockwise. The assumed coordinate system has its X axis pointing to the right, and its Y axis pointing upwards. 
returnPoints  operation flag. In case of a matrix, when the flag is true, the function returns convex hull points. Otherwise, it returns indices of the convex hull points. 
There is a function to check if a curve is convex or not, cv.isContourConvex(). It just return whether True or False. Not a big deal.
There are two types of bounding rectangles.
It is a straight rectangle, it doesn't consider the rotation of the object. So area of the bounding rectangle won't be minimum.
We use the function: cv.boundingRect (points)
points  input 2D point set. 
Here, bounding rectangle is drawn with minimum area, so it considers the rotation also.
We use the function: cv.minAreaRect (points)
points  input 2D point set. 
Next we find the circumcircle of an object using the function cv.minEnclosingCircle(). It is a circle which completely covers the object with minimum area.
We use the functions: cv.minEnclosingCircle (points)
points  input 2D point set. 
cv.circle (img, center, radius, color, thickness = 1, lineType = cv.LINE_8, shift = 0)
img  image where the circle is drawn. 
center  center of the circle. 
radius  radius of the circle. 
color  circle color. 
thickness  thickness of the circle outline, if positive. Negative thickness means that a filled circle is to be drawn. 
lineType  type of the circle boundary. 
shift  number of fractional bits in the coordinates of the center and in the radius value. 
Next one is to fit an ellipse to an object. It returns the rotated rectangle in which the ellipse is inscribed. We use the functions: cv.fitEllipse (points)
points  input 2D point set. 
cv.ellipse1 (img, box, color, thickness = 1, lineType = cv.LINE_8)
img  image. 
box  alternative ellipse representation via RotatedRect. This means that the function draws an ellipse inscribed in the rotated rectangle. 
color  ellipse color. 
thickness  thickness of the ellipse arc outline, if positive. Otherwise, this indicates that a filled ellipse sector is to be drawn. 
lineType  type of the ellipse boundary. 
Similarly we can fit a line to a set of points. We can approximate a straight line to it.
We use the functions: cv.fitLine (points, line, distType, param, reps, aeps)
points  input 2D point set. 
line  output line parameters. It should be a Mat of 4 elements[vx, vy, x0, y0], where [vx, vy] is a normalized vector collinear to the line and [x0, y0] is a point on the line. 
distType  distance used by the Mestimator(see cv.DistanceTypes). 
param  numerical parameter ( C ) for some types of distances. If it is 0, an optimal value is chosen. 
reps  sufficient accuracy for the radius (distance between the coordinate origin and the line). 
aeps  sufficient accuracy for the angle. 0.01 would be a good default value for reps and aeps. 
cv.line (img, pt1, pt2, color, thickness = 1, lineType = cv.LINE_8, shift = 0)
img  image. 
pt1  first point of the line segment. 
pt2  second point of the line segment. 
color  line color. 
thickness  line thickness. 
lineType  type of the line,. 
shift  number of fractional bits in the point coordinates. 