I don't believe we would be able to represent smooth curves with vertical lines like this, due to the fact that the derivative would be undefined. How can we extend this function to do so?
ericlu28
^ I had a similar question when coming across this lecture slide. My initial thought is taking a best-case approximation of the vertical line (slightly angled), and then using that derivative. I'm also curious about how to extend the Cubic Hermite interpolation to vertical lines.
SuryaTalla22
I think in this case the vertical lines indicate position rather than the derivatives. In the case of vertical lines, there probably is a 'special way' to handle those, although approximating this with a really large slope is definitely a possibility.
kujjwal
To what degree is it beneficial to use Hermite interpolation for tasks such as corner or edge detection? If performing splinic interpolation is costly, to what degree is this the best approach with the edge detection task and can we perform interpolation in a cost-effective way for images with lots of curves or high resolutions?
he-yilan
why do we need to get a cubic polynomial? do we get a better result if we also use 2nd derivatives?
JunoLee128
The points are fixed, but how do we find good values for the derivatives? I don't get why the problem is being defined by these four values
zachtam
Cubic Hermite Interpolation can also be used for trajectory generation: computing a finite number of waypoint positions and velocities gives a smooth and valid trajectory.
I don't believe we would be able to represent smooth curves with vertical lines like this, due to the fact that the derivative would be undefined. How can we extend this function to do so?
^ I had a similar question when coming across this lecture slide. My initial thought is taking a best-case approximation of the vertical line (slightly angled), and then using that derivative. I'm also curious about how to extend the Cubic Hermite interpolation to vertical lines.
I think in this case the vertical lines indicate position rather than the derivatives. In the case of vertical lines, there probably is a 'special way' to handle those, although approximating this with a really large slope is definitely a possibility.
To what degree is it beneficial to use Hermite interpolation for tasks such as corner or edge detection? If performing splinic interpolation is costly, to what degree is this the best approach with the edge detection task and can we perform interpolation in a cost-effective way for images with lots of curves or high resolutions?
why do we need to get a cubic polynomial? do we get a better result if we also use 2nd derivatives?
The points are fixed, but how do we find good values for the derivatives? I don't get why the problem is being defined by these four values
Cubic Hermite Interpolation can also be used for trajectory generation: computing a finite number of waypoint positions and velocities gives a smooth and valid trajectory.