The calculation of vanishing point in the verification of the horizontal edge segments Essay

In this section, the increasing horizontal edge segments are used to calculate the vanishing point (VP) to verify the horizontal edge segments, whether these edges are extracted from stair or any other similar visual patterns such as train line and zebra crossing. The VP of a stair can be stated as an imaginary point in a linear perspective drawing in which a set of parallel lines converge. In stairways, the VP can be defined as a point where two handrails of the stair intersect. Basically, the intersection point (x,y) is located outside the stair image(y<0). However, every stair does not have the handrails or some stair have one side handrail. Hence, it is better to construct two virtual handrails instead of depending real handrails. The right and left handrail is the straight line passing through the right and left end points of the lower and upper edge in the horizontal edge segments. Hence, the VP is the intersection point of these two left and right straight lines.
In Fig. 7(c), the left drawing handrail is the straight line passing through the points (x1,y1) and (x2,y2). The equation of the straight line is y = m1x+b1 where, m1 = (y2-y1)/(x2-x1). Similarly, equation y = m2x+b2 is derived from right handrail passing through points (x3,y3) and (x4,y4) where, m2 = (y4-y3)/(x4-x3). Solving these two equations, the intersection point (x,y) is determined which is the vanishing point of the stair. After that, checking the y coordinate of the vanishing point because the vanishing point for the stair will be imaginary (y<0) and will be reside inside the rage of -2IHYVP<0, where IH is the height of the image and YVP is the y-coordinate value of the vanishing point. If the calculating VP resides inside the range, the extracted parallel edge segments certainly indicate a stair. Otherwise, these edge segments may be part of some other stair like object. For example, rail line and zebra crossing have the similar property as stairs. The edges of the rail line are fully horizontal with respect to the ground but the y-coordinate value of the vanishing point both of the rail line and the zebra crossing will be real.
Fig. 8 shows experiment result of rail line and zebra crossing image. In Sample 1, extracted horizontal edges satisfied the three connected point criteria for rail line image that is the property of stair edges. But the calculated vanishing point is (245.05, 85.03) as shown in Fig. 8(e), Sample 1. The y-coordinate of the VP is 85.03. The positive y-coordinate value distinguishes this image from a stair image. In Sample 2 shows that zebra crossing image does not satisfy the three connected point criteria. This is because zebra crossing contains only horizontal edge. And only one vertical edge connected to every horizontal edge. Rail line and zebra crossing VP reside inside of the image as they don't have any slop with respect to ground plane. So the y-coordinate of the VP of the rail line and the zebra crossing is positive.