Vanishing point

[1] Traditional linear drawings use objects with one to three sets of parallels, defining one to three vanishing points.Italian humanist polymath and architect Leon Battista Alberti first introduced the concept in his treatise on perspective in art, De pictura, written in 1435.

If we consider a straight line in space S with the unit vector ns ≡ (nx, ny, nz) and its vanishing point vs, the unit vector associated with vs is equal to ns, assuming both point towards the image plane.

Guidobaldo del Monte gave several verifications, and Humphry Ditton called the result the "main and Great Proposition".

Also, consider a line L that lies in the plane π, which is defined by the equation ax + bz = d. Using perspective pinhole projections, a point on L projected on the image plane will have coordinates defined as, This is the parametric representation of the image L′ of the line L with z as the parameter.

Let A, B, and C be three mutually orthogonal straight lines in space and vA ≡ (xA, yA, f), vB ≡ (xB, yB, f), vC ≡ (xC, yC, f) be the three corresponding vanishing points respectively.

The orthocenter of the triangle with vertices in the three vanishing points is the intersection of the optical axis and the image plane.

The Gaussian sphere has accumulator cells that increase when a great circle passes through them, i.e. in the image a line segment intersects the vanishing point.

Several modifications have been made since, but one of the most efficient techniques was using the Hough Transform, mapping the parameters of the line segment to the bounded space.

The process of mapping from the image to the bounded spaces causes the loss of the actual distances between line segments and points.

In the search step, the accumulator cell with the maximum number of line segments passing through it is found.

1.	The width of the side street, W is computed from the known widths of the adjacent shops.
2.	As a vanishing point , V is visible, the width of only one shop is needed.