Could you explain again what the alpha is there for?
mpotoole
First, recall that homogeneous coordinates are defined up to a scale ambiguity, i.e., $(x,y,1) \equiv (sx,sy,s)$.
In the slide, the result of multiplying the matrix $H$ with homogeneous coordinate $[x,y,1]$ will produce a homogeneous coordinate $\frac{1}{\alpha}[x',y',1]$ for some $\alpha \neq 0$. However, the third component of this vector is not typically $1$. So $\alpha$ is simply rescaling the equation such that it produces a homogeneous coordinate in normalized form.
Could you explain again what the alpha is there for?
First, recall that homogeneous coordinates are defined up to a scale ambiguity, i.e., $(x,y,1) \equiv (sx,sy,s)$.
In the slide, the result of multiplying the matrix $H$ with homogeneous coordinate $[x,y,1]$ will produce a homogeneous coordinate $\frac{1}{\alpha}[x',y',1]$ for some $\alpha \neq 0$. However, the third component of this vector is not typically $1$. So $\alpha$ is simply rescaling the equation such that it produces a homogeneous coordinate in normalized form.
Thank you