Optical Illusions - Introduction

Introduction

Errors in Image Intensity

Errors in Line Estimation

Errors in Movement

Erroneous Shape Estimation

Errors in Line Estimation

Luckiesh Pattern

Figure 1: Click repeatedly on the figure to see zoom ins illustrating the fitting of the curve.

As you can see, in this pattern the circle appears to be distorted. This is predicted by the bias in the estimation of the intersection points between the circle and the lines of the background.

The estimation of the circle requires a few computations which we modeled as follows:

First the intersection points between background edges and circle edges are computed, where arcs between two consecutive background lines were approximated by straight lines.
Next, consecutive intersection points are calculated. One originating from an obtuse angle and one from an acute angle. They are then connected with straight line segments.
Last, Bezier splines are fit to these line segments.

Luckiesh Pattern in Motion

Figure 2: Click on the pattern and move your cursor to change the orientation of the background lines.

Since the value of the bias depends on the direction of the intersecting lines, changing the direction of the background lines causes a change in the bias and thus a change in the estimated curve, with the circle bumping at different locations.



Introduction Errors in Image Intensity Errors in Line Estimation The Theory Poggendorff Illusion Zöllner Illusion Luckiesh Pattern Errors in Movement Erroneous Shape Estimation	Errors in Line Estimation Luckiesh Pattern Figure 1: Click repeatedly on the figure to see zoom ins illustrating the fitting of the curve. As you can see, in this pattern the circle appears to be distorted. This is predicted by the bias in the estimation of the intersection points between the circle and the lines of the background. The estimation of the circle requires a few computations which we modeled as follows: First the intersection points between background edges and circle edges are computed, where arcs between two consecutive background lines were approximated by straight lines. Next, consecutive intersection points are calculated. One originating from an obtuse angle and one from an acute angle. They are then connected with straight line segments. Last, Bezier splines are fit to these line segments. Luckiesh Pattern in Motion Figure 2: Click on the pattern and move your cursor to change the orientation of the background lines. Since the value of the bias depends on the direction of the intersecting lines, changing the direction of the background lines causes a change in the bias and thus a change in the estimated curve, with the circle bumping at different locations.