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THIS PAPER PRESENTS AN EFFICIENT METHOD THAT CAN BE IMPLEMENTED IN A FIXTURELESS MACHINE VISION SYSTEM TO INSPECT MACHINED PARTS. THE PROPOSED METHOD UTILIZES THE PRIOR KNOWLEDGE ABOUT THE SHAPE OF THE PART TO LIMIT THE SIZE OF THE PARAMETER SPACE THAT NEEDS TO BE QUANTIZED WHEN THE HOUGH TRANSFORM METHOD IS USED. THE PROPOSED METHOD CAN REPRESENT A PART'S OUTLINE, REGARDLESS OF THE PART'S POSITION, IN TERMS OF STRAIGHT LINES AND PARTIAL CURVES AT A HIGH SPEED.