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how to reduce vertices of polygon keep the shape same as much as possible

Capture.PNG i have tried both of these ways pchip(red) and Savitzky-Golay filter(blue) : for polygons.i have problem that the number of vertices of polygons are very high after reading boundaries from image .how can i reduce the number of vertices keeping the shape of the polygons same as much as possible.

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One way is to use a compression algorithm such as Fan Data Compression which is a simple algorithm where you just continue in a straight line until the deviation exceeds a certain threshold, and then you start again.

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