The Inversion of Figure and Ground

Rubin’s vase is the well known example of the inversion of figure and ground.  The next figure shows it.

When we regard the black region as the figure, we see the vase. Inversely, when we regard the white region as the figure, we see two faces.  According to Figure-Ground (Perception) in Wikipedia, the perceived figure depends on the direction of the edge. If edges are assigned inward, the black vase is perceived. On the other hand, if edges are assigned outward, two white faces are perceived.　The edge is critical for the cognition of the 3D object. However, it isn’t the substance. Considering the above example, there is nothing between the white area and the black area.

The left side of the above figure shows the borderline between black region and white region. The right side of the above figure is the magnified view. Evidently, there is nothing between black pixels and white pixels.

However, our brain cannot handle well the blank edge. Thus, our brain  substantializes it to handle it. The next figure shows the substantialized edge of the vase or two faces.

In the above figure, the blank edge is converted into the line. This conversion is the basis of line drawings. Especially, the most simplified drawing consists of only edges. The above figure is an example. Even though it is very simple, it keeps the ambiguity. So, it seems the vase or two faces. That is, because the edge is originally blank, the edge itself doesn’t have the direction. If both directions can be interpreted to suit the familiar object, the inversion of figure and ground occurs.

Next, let us consider the conversion of the blank edge into the line in the geometry. Euclid defines the line in Elements as follows.

Definition 2. A line is a length without breadth.

That is, Euclidean line corresponds to the blank edge. However, if we use the Euclidean line, we cannot draw any figure. As a result, we draw figures using substantial lines. The theoretical validity of the conversion is given by the next figure.

The above figure represents the conversion of the edge into the line on the computer graphics. Two pixels are at least necessary for an edge. In contrast, the line requires only one pixel width. A line is more effective than an edge for the data storage. Moreover, if we  regard the size of the tip of a pencil as the size of the dot,  similar logic is applicable to traditional  paper and pencil geometry.