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We present a novel metric Spatial Recall Index to assess the performance of machine-learning (ML) algorithms for automotive applications, focusing on where in the image which performance occurs. Typical metrics like intersection-over-union (IoU), precisionrecallcurves or average precision (AP) quantify the performance over a whole database of images, neglecting spatial performance variations. But as the optics of camera systems are spatially variable over the field of view, the performance of ML-based algorithms is also a function of space, which we show in simulation: A realistic objective lens based on a Cooke-triplet that exhibits typical optical aberrations like astigmatism and chromatic aberration, all variable over field, is modeled. The model is then applied to a subset of the BDD100k dataset with spatially-varying kernels. We then quantify local changes in the performance of the pre-trained Mask R-CNN algorithm. Our examples demonstrate the spatial dependence of the performance of ML-based algorithms from the optical quality over field, highlighting the need to take the spatial dimension into account when training ML-based algorithms, especially when looking forward to autonomous driving applications.
Spatial precision and recall indices to assess the performance of instance segmentation algorithms
(2022)
We had already demonstrated a numerical model for the point spread function (PSF) of an optical system that can efficiently model both the experimental measurements and the lens design simulations of the PSF. The novelty lies in the portability and the parameterization of this model, which allow for completely new ways to validate optical systems, which is especially interesting not only for mass production optics such as in the automotive industry but also for ophthalmology. The numerical basis for this model is a nonlinear regression of the PSF with an artificial neural network (ANN). After briefly describing both the principle and the applications of the model, we then discuss two optically important aspects: the spatial resolution and the accuracy of the model. Using mean squared error (MSE) as a metric, we vary the topology of the neural network, both in the number of neurons and in the number of hidden layers. Measurement and simulation of a PSF can have a much higher spatial resolution than the typical pixel size used in current camera sensors. We discuss the influence this has on the topology of the ANN. The relative accuracy of the averaged pixel MSE is below 10 − 4, thus giving confidence that the regression does indeed model the measurement data with good accuracy. This article is only the starting point, and we propose several research avenues for future work.