Hough transform of equilateral triangles
There are a few related errors in the description of the Hough representation of equilateral triangles in slide 40, slide 41, and the solution hints to IN5520/9520 Exam 2019 Exercise 3c. The peaks in the Hough representation will be π/3 apart along the θ-axis (so the descriptions are correct on that), but the associated values along the ρ-axis will alternative between being positive and negative with constant absolute value (the descriptions incorrectly state that the ρ-values are constant).
In order to rectify this, the following two changes should be applied to slide 40:
1. From: "The normals onto the three sides are of the same length, => ρ=h"
to: "The normals onto the three sides are of the same length, => abs(ρ)=h"
2. From "A: The three maxima in the (θ,ρ)-domain will slide in the positive θ-direction, keeping the 60 degree (π/3) distance between the maxima and a constant ρ-value, sliding out of the [-π/2,π/2]-domain at π/2 and reappearing at –π/2."
to: "A: The three maxima in the (θ,ρ)-domain will slide in the positive θ-direction, keeping the 60 degree (π/3) distance between the maxima and a constant absolute ρ-value, sliding out of the [-π/2,π/2]-domain at π/2 and reappearing at –π/2 with opposite sign for the ρ-value."
Correspondingly, the following change should be applied to slide 41:
From: "The three maxima will now have different, but constant ρ-values, sliding out of the [-π/2,π/2]-domain at π/2 and re-appearing at –π/2."
to: "The three maxima will now have different, but constant absolute ρ-values, sliding out of the [-π/2,π/2]-domain at π/2 and re-appearing at –π/2 with opposite sign for the ρ-value."
Finally, the following change should be applied to the solution hints to IN5520/9520 Exam 2019 Exercise 3c:
From: "The normal onto the three sides are of the same length, => all peaks occur at ρ=h."
to: "The normal onto the three sides are of the same length, => all peaks occur at abs(ρ)=h."
Sorry for any confusion this might have caused you, and thanks to Hilmar R. Widerberg for pointing it out!