Tag Archives: sfrmat

Minimalist ESF, LSF, MTF by Monotonic Regression

Because the Slanted Edge Method of estimating the Spectral Frequency Response of a camera and lens is one of the more popular articles on this site, I have fielded variations on the following question many times over the past ten years:

How do you go from the intensity cloud  produced by the projection of a slanted edge captured in a raw file to a good estimate of the relevant Line Spread Function?

Figure 1.  Slanted edge captured in the raw data and projected to the edge normal.  The data noisy because of shot noise and PRNU.  How to estimate the underlying edge profile (orange line, the Edge Spread Function)?

So I decided to write down the answer that I have settled on.  It relies on monotone spline regression to obtain an Edge Spread Function (ESF) and then reuses the parameters of the regression to infer the relative regularized Line Spread Function (LSF) analytically in one go.

This front-loads all uncertainty to just the estimation of the ESF since the other steps on the way to the SFR become purely mechanical.  In addition the monotonicity constraint puts some guardrails around the curve, keeping it on the straight and narrow without further effort.

This minimalist, what-you-see-is-what-you-get approach gets around the usual need for signal conditioning such as binning, finite difference calculations and other filtering, with their drawbacks and compensations.  It has the potential to be further refined so consider it a hot-rod DIY kit.  Even so it is an intuitively direct implementation of the method and it provides strong validation for Frans van den Bergh’s open source MTF Mapper, the undisputed champ in this space,[1] as it produces very similar results with raw slanted edge captures. Continue reading Minimalist ESF, LSF, MTF by Monotonic Regression

MTF Mapper vs sfrmat3

Over the last couple of years I’ve been using Frans van den Bergh‘s excellent open source MTF Mapper to measure the Modulation Transfer Function of imaging systems off a slanted edge target, as you may have seen in these pages.  As long as one understands how to get the most out of it I find it a solid product that gives reliable results, with MTF50 typically well within 2% of actual in less than ideal real-world situations (see below).  I had little to compare it to other than to tests published by gear testing sites:  they apparently mostly use a commercial package called Imatest for their slanted edge readings – and it seemed to correlate well with those.

Then recently Jim Kasson pointed out sfrmat3, the matlab program written by Peter Burns who is a slanted edge method expert who worked at Kodak and was a member of the committee responsible for ISO12233, the resolution and spatial frequency response standard for photography.  sfrmat3 is considered to be a solid implementation of the standard and many, including Imatest, benchmark against it – so I was curious to see how MTF Mapper 0.4.1.6 would compare.  It did well.

Continue reading MTF Mapper vs sfrmat3