Real-time FPGA-based implementation of the AKAZE algorithm with nonlinear scale space generation using image partitioning

The first step in a scale invariant image matching system is scale space generation. Nonlinear scale space generation algorithms such as AKAZE, reduce noise and distortion in different scales while retaining the borders and key-points of the image. An FPGA-based hardware architecture for AKAZE nonlinear scale space generation is proposed to speed up this algorithm for real-time applications. The three contributions of this work are (1) mapping the two passes of the AKAZE algorithm onto a hardware architecture that realizes parallel processing of multiple sections, (2) multi-scale line buffers which can be used for different scales, and (3) a time-sharing mechanism in the memory management unit to process multiple sections of the image in parallel. We propose a time-sharing mechanism for memory management to prevent artifacts as a result of separating the process of image partitioning. We also use approximations in the algorithm to make hardware implementation more efficient while maintaining the repeatability of the detection. A frame rate of 304 frames per second for a $$1280 \times 768$$ 1280 × 768 image resolution is achieved which is favorably faster in comparison with other work.

modglm: An R package for testing, interpreting, and displaying interactions in generalized linear models of discrete data

Many researchers hope to examine interaction effects using generalized linear models (GLMs) to predict outcomes on nonlinear scales. For instance, logistic and Poisson GLMs are used to estimate associations between predictors and outcomes in nonlinear probability and count scales, respectively. However, we (McCabe et al., 2021; Halvorson et al., in press) and others (Ai & Norton, 2003; Mize, 2019; Norton, Wang, & Ai, 2004) have shown that testing and interpreting interaction effects on these scales is not straightforward. GLMs require the application of partial derivatives and/or discrete differences to compute and probe interaction effects appropriately when models are interpreted on their nonlinear scale. Currently available open-source software does not provide methods of computing these interaction effects on probability and count scales, reflecting a central limitation in applying these methods in research practice. Here, we introduce `modglm`, an R-based software package that accompanies our manuscript providing recommendations for computing interaction effects in nonlinear probability and counts (McCabe et al., 2021). This software produces the interaction effect between two variables in generalized linear models of probabilities and counts and provides additional statistics and plotting utilities for evaluating and describing this effect.

Optimized Multi-Position Calibration Method with Nonlinear Scale Factor for Inertial Measurement Units

Navigation grade inertial measurement units (IMUs) should be calibrated after Inertial Navigation Systems (INSs) are assembled and be re-calibrated after certain periods of time. The multi-position calibration methods with advantage of not requiring high-precision equipment are widely discussed. However, the existing multi-position calibration methods for IMU are based on the model of linear scale factors. To improve the precision of INS, the nonlinear scale factors should be calibrated accurately. This paper proposes an optimized multi-position calibration method with nonlinear scale factor for IMU, and the optimal calibration motion of IMU has been designed based on the analysis of sensitivity of the cost function to the calibration parameters. Besides, in order to improve the accuracy and robustness of the optimization, an estimation method on initial values is presented to solve the problem of setting initial values for iterative methods. Simulations and experiments show that the proposed method outperforms the calibration method without nonlinear scale factors. The navigation accuracy of INS can be improved by up to 17% in lab conditions and 12% in the moving vehicle experiment, respectively.

Counterexamples in scale calculus

We construct counterexamples to classical calculus facts such as the inverse and implicit function theorems in scale calculus—a generalization of multivariable calculus to infinite-dimensional vector spaces, in which the reparameterization maps relevant to symplectic geometry are smooth. Scale calculus is a corner stone of polyfold theory, which was introduced by Hofer, Wysocki, and Zehnder as a broadly applicable tool for regularizing moduli spaces of pseudoholomorphic curves. We show how the novel nonlinear scale-Fredholm notion in polyfold theory overcomes the lack of implicit function theorems, by formally establishing an often implicitly used fact: The differentials of basic germs—the local models for scale-Fredholm maps—vary continuously in the space of bounded operators when the base point changes. We moreover demonstrate that this continuity holds only in specific coordinates, by constructing an example of a scale-diffeomorphism and scale-Fredholm map with discontinuous differentials. This justifies the high technical complexity in the foundations of polyfold theory.