It is a shame that such small tweaks is always a non-existent man-page away with PHP's ImageMagick wrapper. (Using spline could smooth out a lot of straight and thin edges, but, as it is, I will never find out.)
For resizing operation you use a resampling filter, not an interpolation method. E.g. the 'point' filter corresponds to the 'nearest' interpolation. http://www.imagemagick.org/Usage/filter/
To set interpolation for e.g. rotation operations, you'd use the setImageInterpolateMethod method:
http://php.net/manual/en/imagick.resizeimage.php
It is a shame that such small tweaks is always a non-existent man-page away with PHP's ImageMagick wrapper. (Using spline could smooth out a lot of straight and thin edges, but, as it is, I will never find out.)