A Linear option allows the blur or sharpen effect to extend from a central line.SILKYPIX JP 9 FeatureSILKYPIX Developer Studio Pro10 Feature

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 a photo before the linear effect is applied.
Photo Before Blur / Sharpen Periphery Tool applied.

Here is the same image after Blur Periphery is applied with the Linear option.

After applying the Blur / Sharpen Periphery Tool with the Linear effect option.