  Computer vision methods typically optimize for first-order dynamics (e.g.,
optical flow). However, in many cases the properties of interest are subtle
variations in higher-order changes, such as acceleration. This is true in the
cardiac pulse, where the second derivative can be used as an indicator of blood
pressure and arterial disease. Recent developments in camera-based vital sign
measurement have shown that cardiac measurements can be recovered with
impressive accuracy from videos; however, most of the research has focused on
extracting summary statistics such as heart rate. Less emphasis has been put on
the accuracy of waveform morphology that is necessary for many clinically
meaningful assessments. In this work, we provide evidence that higher-order
dynamics are better estimated by neural models when explicitly optimized for in
the loss function. Furthermore, adding second-derivative inputs also improves
performance when estimating second-order dynamics. We illustrate this, by
showing that incorporating the second derivative of both the input frames and
the target vital sign signals into the training procedure, models are better
able to estimate left ventricle ejection time (LVET) intervals.
