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Reduce density of points in ROI using Ramer–Douglas–Peucker algorithm



P_reduced = reducepoly(P) reduces the density of points in array P. The reducepoly function uses the Ramer-Douglas-Peucker line simplification algorithm, removing points along straight lines and leaving only knickpoints (points where the line curves).

P_reduced = reducepoly(P,tolerance) reduces the density of points in array P, where tolerance specifies how much a point can deviate from a straight line.


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Read an image into the workspace.

I = imread('coins.png');

Figure contains an axes. The axes contains an object of type image.

Convert the image from grayscale to binary.

bw = imbinarize(I);

Obtain the boundaries of all the coins in the binary image.

[B,L] = bwboundaries(bw,'noholes');

Select the boundary of the first detected coin.

coinNumber = 1;
boundary = B{coinNumber};

Plot the boundary for the first detected coin over the original image.

hold on
xlim([min(boundary(:,2))-10 max(boundary(:,2))+10])
ylim([min(boundary(:,1))-10 max(boundary(:,1))+10])
hold off

Figure contains an axes. The axes contains 3 objects of type line, image.

Use reducepoly to reduce the number of points defining the coin boundary. Return a smaller number of points by increasing the tolerance from the default value of 0.001.

tolerance = 0.02;
p_reduced = reducepoly(boundary,tolerance);

To see how well the reduced polygon matches the original polygon, plot the reduced polygon vertices over the image.

line(p_reduced(:,2),p_reduced(:,1), ...
title('Original Polygon (Red) and Reduced Polygon (Blue)');

Figure contains an axes. The axes with title Original Polygon (Red) and Reduced Polygon (Blue) contains 4 objects of type line, image.

Input Arguments

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Points to be reduced, specified as an n-by-2 numeric matrix of the form [x1 y1; ...; xn yn]. Each row in the array defines a vertex in an ROI shape, such as a polyline, polygon, or freehand.

For example, you can draw a freehand ROI by using the drawfreehand function. Then, get the ROI vertices from the Position property of the freehand ROI object.

roi = drawfreehand;
P = roi.Position;

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Sensitivity of the reduction algorithm, specified as a numeric scalar in the range [0, 1]. Increasing the tolerance increases the number of points removed. A tolerance value of 0 has a minimum reduction in points. A tolerance value of 1 results in maximum reduction in points, leaving only the end points of the line.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

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Reduced data set, returned as an m-by-2 numeric matrix. The number of reduced points is usually smaller than the number of original points in P.

Data Types: double


The Ramer-Douglas-Peucker line simplification algorithm recursively subdivides a shape looking to replace a run of points with a straight line. The algorithm checks that no point in the run deviates from the straight line by more than the value specified by tolerance.

Introduced in R2019b