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If I have an object consisting by a set of vertices [tex]V[/tex], and I calculate the principal axis for the object and get the three principal axis [tex]{\bf e}_1, {\bf e}_2, {\bf e}_3[/tex] by eigen-decomposing the covariance [tex]\sigma=V^T V[/tex]. The problem is the ambiguity of the axis direction.

My solution to this is force [tex]e_{11}, e_{21}[/tex] to be positive, and change the rest components of [tex]{\bf e}_1, {\bf e}_2[/tex] respectively. Then, the third eigen vector [tex]{\bf e}_3[/tex] can be defined correspondingly.

By doing that, is the pose of the object fixed and uniqe? And do the set of principal axis have freedom of two please?

Any one help me with this problem please?

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# Principal Axis Alignment Problem

Can you offer guidance or do you also need help?

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