In real world uses, QR Codes are printed or overlaid on top of complex surfaces, like cylindrical bottles or other daily objects with random topographies that pose big challenges to their readout with the conventional planar algorithms proposed in the standard ISO and implemented in most of the available codes. We propose here a general-purpose method to improve the readability of QR Codes placed on these challenging surfaces, by fitting the topography of the underlying arbitrary surface with thin-plate splines. Then, we compare this new method with other alternatives proposed in the literature, like affine, projective and cylindrical transformations. Results demonstrate that our new approach works well under a variety of arbitrary surface topographies including those assumed in former proposals, and improve their readability by a factor of 4, clearly outperforming state-of-the-art decoders.

Image color consistency is the key problem in digital imaging consistency when creating datasets. Here, we propose an improved 3D Thin-Plate Splines (TPS3D) color correction method to be used, in conjunction with color charts (i.e. Macbeth ColorChecker) or other machine-readable patterns, to achieve image consistency by post-processing. Also, we benchmark our method against its former implementation and the alternative methods reported to date with an augmented dataset based on the Gehler's ColorChecker dataset. Benchmark includes how corrected images resemble the ground-truth images and how fast these implementations are. Results demonstrate that the TPS3D is the best candidate to achieve image consistency. Furthermore, our Smooth-TPS3D method shows equivalent results compared to the original method and reduced the 11-15% of ill-conditioned scenarios which the previous method failed to less than 1%. Moreover, we demonstrate that the Smooth-TPS method is 20% faster than the original method. Finally, we discuss how different methods offer different compromises between quality, correction accuracy and computational load.

Free chlorine (FC) plays a crucial role in ensuring the safety of drinking water by effectively inactivating pathogenic microorganisms. However, traditional methods for measuring FC levels often require specialized equipment and laboratory settings, limiting their accessibility and practicality for on-site or point-of-use monitoring. QR Codes are powerful machine-readable patterns that are used worldwide to encode information (i.e., URLs or IDs), but their computer vision features allow QR Codes to act as carriers of other features for several applications. Often, this capability is used for aesthetics, e.g., embedding a logo in the QR Code. In this work, we propose using our technique to build back-compatible Color QR Codes, which can embed dozens of colorimetric references, to assist in the color correction to readout sensors. Specifically, we target two well-known products in the HORECA (hotel/restaurant/café) sector that qualitatively measure chlorine levels in samples of water. The two targeted methods were a BTB strip and a DPD powder. First, the BTB strip was a pH-based indicator distributed by Sensafe^®, which uses the well-known bromothymol blue as a base-reactive indicator; second, the DPD powder was a colorimetric test distributed by Hach^®, which employs diethyl-p-phenylenediamine (DPD) to produce a pink coloration in the presence of free chlorine. Custom Color QR Codes were created for both color palettes and exposed to several illumination conditions, captured with three different mobile devices and tested over different water samples. Results indicate that both methods could be correctly digitized in real-world conditions with our technology, rendering a 88.10% accuracy for the BTB strip measurement, and 84.62% for the DPD powder one.

A sketch is a category equipped with specified collections of cones and cocones. Its models are functors to the category of sets that send the distinguished cones and cocones to limit cones and colimit cocones, respectively. Sketches provide a categorical formalization of theories, interpreting logical operations in terms of limits and colimits. Gabriel and Ulmer showed that categories of models of sketches involving only cones (called limit sketches) are precisely the locally presentable categories, while Lair extended this correspondence to sketches including both cones and cocones, thereby characterizing accessible categories. In this article, we discuss a homotopy-coherent generalization of sketches in the context of $\infty$-categories and prove that presentable $\infty$-categories are the $\infty$-categories of models of limit sketches, whereas accessible $\infty$-categories arise as the $\infty$-categories of models of arbitrary sketches. As illustrations, we make the corresponding sketches explicit for a wide range of $\infty$-categories, including complete Segal spaces, $\infty$-operads, $A_\infty$-algebras, $E_\infty$-algebras, spectra, and higher sheaves.