The images below illustrate the change in the direction of the gradient on a grayscale circle. When the sign of G x {\displaystyle \mathbf {G_{x}} } and G y {\displaystyle \mathbf {G_{y}} } are the same the gradient's angle is positive, and negative when different. In the example below the red and yellow colors on the edge of the circle indicate positive angles, and the blue and cyan colors indicate negative angles. The vertical edges on the left and right sides of the circle have an angle of 0 because there is no local change in G y {\displaystyle \mathbf {G_{y}} } . The horizontal edges at the top and bottom sides of the circle have angles of − π / 2 and π / 2 respectively because there is no local change in G x {\displaystyle \mathbf {G_{x}} } . The negative angle for top edge signifies the transition is from a bright to dark region, and the positive angle for the bottom edge signifies a transition from a dark to bright region. All other pixels are marked as black due to no local change in either G x {\displaystyle \mathbf {G_{x}} } or G y {\displaystyle \mathbf {G_{y}} } , and thus the angle is not defined. It should be noted that since the angle is a function of the ratio of G y {\displaystyle \mathbf {G_{y}} } to G x {\displaystyle \mathbf {G_{x}} } pixels with small rates of change can still have a large angle response. As a result noise can have a large angle response which is typically undesired. When using gradient angle information for image processing applications effort should be made to remove image noise to reduce this false response.

In August 2008, the London Transport Commissioner Peter Hendy announced that the withdrawal of the bendy buses would take place, starting in 2009. So as to reduce additional costs to TfL, the buses would be withdrawn as their 5-year operating contracts came up for renewal, with the replacement types being decided by operators. Options for replacement would not preclude such measures as tri-axle buses . However, research has indicated that removing articulated vehicles may not be without cost; London Travel Watch undertook a study in September 2008 which found that to replace articulated vehicles on three bus routes, and maintain overall route capacity, would cost an additional £ per annum, due to the additional vehicles necessitated. [16]