in this example the single straight line 200 is the focus of our u201c attention u201d as illustrated in fig1 a several hypotheses transforms 202 are generated and rejected as illustrated in fig1 b 11e before a hypothesis is verified as shown in fig1 f as seen from the figures attempts to find the line 200 are made on various line segments of the target image the hypothesis is rejected until the proper line segment 200 is found in the target image if a reference pattern object has n straight lines also referred to herein as u201c icons u201d and the scene image has a m straight lines lines belong to object s we want to recognize and locate plus noise lines then the cost for using one reference line as a hypothesis is 0 m and for using all reference lines is 0 n u00d7 m if we train on k object then the computation cost for each hypothesis is 0 m u00d7 k and the total computation cost is 0 n u00d7 m u00d7 k these costs assume no prior knowledge of the transformation between two compared lines however we often do have a priori information that limits the range of transformations for example if we know that the target objects will only vary in scale with in a range of 0 5 to 2 0 then many possible pairs of line matches transformations can be immediately eliminated another way to reduce the number of hypotheses is to.