A little while ago, I needed to find the rotation angle of a flat object in an image, so sampling the edge and finding the line was the way to go. What I eventually went with was:

use strict;
use warnings;
use Statistics::LineFit;
use Math::Trig;

...
    my $lineFit = Statistics::LineFit->new();
    my @x = map {$_->{col}} @edgeSamples;
    my @y = map {$_->{row}} @edgeSamples;

unless ($lineFit->setData(\@x, \@y))
    {
        print "Invalid data sample for regression; could not calculate
+ skew for $inFile\n";
        next;
    }
...
    my ($intercept, $slope) = $lineFit->coefficients();
    my $angle = atan($slope);
    $angle *= 180/3.14159265359;
...
[download]

Now, that does linear interpolation, but I would expect mass loss to be more of a noisy exponential decay towards the final value than linear. If it turns out to actually be a problem you could try resorting to piecewise linear interpolation, or use a fancy high-order plotting package.