A Linear option allows the blur or sharpen effect to extend from a central line.
The Blur / Sharpen Periphery Tool lets you establish a center point of an area of your photo, then apply a blur or sharpen adjustment to the area. The area of effect can be adjusted in size. You can also reset the center point of the area. The new Linear option applies the effect extending from a customizable line. You can also specify the angle of the blur or sharpen direction.
Here is the same image after Blur Periphery is applied with the Linear option.