{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T18:55:59Z","timestamp":1791831359694,"version":"4.3.4"},"reference-count":31,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T00:00:00Z","timestamp":1784851200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"John von Neumann University (NJE), Kecskem\u00e9t,\u00a0Hungary"},{"id":[{"id":"https:\/\/ror.org\/03n9qzd79","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Camera and LiDAR sensors in safety-critical autonomous systems suffer undetected distributional shifts that silently corrupt downstream perception. Out-of-distribution (OOD) detection is the established sensor-data-integrity primitive, but no single post hoc detector covers every shift type, and existing detectors lack guarantees on their false-positive rate (FPR). This paper asks when calibrated score fusion helps and provides a distribution-free finite-sample FPR certificate. Four post hoc scores\u2014Maximum Softmax Probability (MSP), Energy, Mahalanobis distance and k-nearest-neighbour (KNN) distance\u2014are calibrated to p-values by the empirical cumulative distribution function (ECDF) and combined by Fisher\u2019s method or cross-backbone z-score averaging, then wrapped in a conformal predictor with Hoeffding-based Probably Approximately Correct (PAC) bounds. On the full-split PUG camera benchmark (215,040 images), uniform same-backbone p-value fusion does not beat the best single detector (Mahalanobis); the gain comes from cross-backbone diversity: a z-score average of Mahalanobis distances over ResNet-50 and frozen DINOv2 reaches a mean area-under-the-ROC-curve (AUROC) of 0.9258 (+0.0199), rising to 0.9292 (+0.0233) with added spectral and dropout signals (DeLong p&lt;10\u22129). On the nuScenes LiDAR sensor (256,873 frames), uniform fusion yields only a small, calibration-sensitive gain over the best single detector (MSP), so the substantial fusion gain is confined to cross-backbone averaging on the camera. The distribution-free PAC certificate, by contrast, transfers across both sensors with margins below 1.5% (0.96% camera, 0.25% LiDAR), giving evidence usable in ISO 26262 and EASA CoDANN safety cases.<\/jats:p>","DOI":"10.3390\/s26154706","type":"journal-article","created":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T10:38:41Z","timestamp":1784889521000},"page":"4706","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["When Does Score Fusion Help? Conformally Certified Out-of-Distribution Detection for Camera and LiDAR Sensors"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-9587-4981","authenticated-orcid":false,"given":"Lor\u00e1nt","family":"Szab\u00f3","sequence":"first","affiliation":[{"name":"AI Research Center, John von Neumann University, 6000 Kecskem\u00e9t, Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6366-8281","authenticated-orcid":false,"given":"Zolt\u00e1n","family":"Weltsch","sequence":"additional","affiliation":[{"name":"Department of Road and Rail Vehicles, Sz\u00e9chenyi Istv\u00e1n University, 9026 Gy\u0151r, Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-8546-718X","authenticated-orcid":false,"given":"Andrea","family":"\u00c1d\u00e1mn\u00e9-Major","sequence":"additional","affiliation":[{"name":"AI Research Center, John von Neumann University, 6000 Kecskem\u00e9t, Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"32598","DOI":"10.52202\/068431-2362","article-title":"OpenOOD: Benchmarking Generalized Out-of-Distribution Detection","volume":"35","author":"Yang","year":"2022","journal-title":"Adv. Neural Inf. Process. Syst. (Neurips) Datasets Benchmarks Track"},{"key":"ref_2","unstructured":"Hendrycks, D., and Gimpel, K. (2017, January 24\u201326). A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks. Proceedings of the 5th International Conference on Learning Representations (ICLR), Toulon, France."},{"key":"ref_3","first-page":"1","article-title":"OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detection","volume":"2","author":"Zhang","year":"2024","journal-title":"J. Data Centric Mach. Learn. Res. (DMLR)"},{"key":"ref_4","first-page":"21464","article-title":"Energy-based Out-of-distribution Detection","volume":"33","author":"Liu","year":"2020","journal-title":"Proc. Adv. Neural Inf. Process. Syst. (NeurIPS)"},{"key":"ref_5","first-page":"7167","article-title":"A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks","volume":"31","author":"Lee","year":"2018","journal-title":"Proc. Adv. Neural Inf. Process. Syst. (NeurIPS)"},{"key":"ref_6","unstructured":"Sun, Y., Ming, Y., Zhu, X., and Li, Y. (2022, January 17\u201323). Out-of-Distribution Detection with Deep Nearest Neighbors. Proceedings of the 39th International Conference on Machine Learning (ICML), Baltimore, MD, USA."},{"key":"ref_7","unstructured":"Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., and Clark, J. (2021, January 18\u201324). Learning Transferable Visual Models From Natural Language Supervision. Proceedings of the 38th International Conference on Machine Learning (ICML), Virtual."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"35087","DOI":"10.52202\/068431-2543","article-title":"Delving into Out-of-Distribution Detection with Vision-Language Representations","volume":"35","author":"Ming","year":"2022","journal-title":"Proc. Adv. Neural Inf. Process. Syst. (NeurIPS)"},{"key":"ref_9","unstructured":"Vovk, V., Gammerman, A., and Shafer, G. (2005). Algorithmic Learning in a Random World, Springer."},{"key":"ref_10","unstructured":"Fisher, R.A. (1925). Statistical Methods for Research Workers, Oliver and Boyd."},{"key":"ref_11","unstructured":"Stouffer, S.A., Suchman, E.A., DeVinney, L.C., Star, S.A., and Williams, R.M. (1949). The American Soldier: Adjustment During Army Life, Princeton University Press."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1561\/2200000101","article-title":"Conformal Prediction: A Gentle Introduction","volume":"16","author":"Angelopoulos","year":"2023","journal-title":"Found. Trends Mach. Learn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1214\/22-AOS2244","article-title":"Testing for Outliers with Conformal p-values","volume":"51","author":"Bates","year":"2023","journal-title":"Ann. Stat."},{"key":"ref_14","unstructured":"Liang, S., Li, Y., and Srikant, R. (May, January 30). Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks. Proceedings of the 6th International Conference on Learning Representations (ICLR), Vancouver, BC, Canada."},{"key":"ref_15","unstructured":"Gal, Y., and Ghahramani, Z. (2016, January 19\u201324). Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning. Proceedings of the 33rd International Conference on Machine Learning (ICML), New York, NY, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"987","DOI":"10.2307\/2529826","article-title":"A Method for Combining Non-Independent, One-Sided Tests of Significance","volume":"31","author":"Brown","year":"1975","journal-title":"Biometrics"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1080\/01621459.1963.10500830","article-title":"Probability Inequalities for Sums of Bounded Random Variables","volume":"58","author":"Hoeffding","year":"1963","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_18","first-page":"17959","article-title":"PUG: Photorealistic and Semantically Controllable Synthetic Data for Representation Learning","volume":"36","author":"Bordes","year":"2023","journal-title":"Proc. Adv. Neural Inf. Process. Syst. (NeurIPS)"},{"key":"ref_19","unstructured":"Krizhevsky, A. (2009). Learning Multiple Layers of Features from Tiny Images. Technical Report, University of Toronto."},{"key":"ref_20","unstructured":"Netzer, Y., Wang, T., Coates, A., Bissacco, A., Wu, B., and Ng, A.Y. (2011, January 16). Reading Digits in Natural Images with Unsupervised Feature Learning. Proceedings of the NeurIPS Workshop on Deep Learning and Unsupervised Feature Learning, Sierra Nevada, Spain."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep Residual Learning for Image Recognition. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_22","unstructured":"Oquab, M., Darcet, T., Moutakanni, T., Vo, H., Szafraniec, M., Khalidov, V., Fernandez, P., Haziza, D., Massa, F., and El-Nouby, A. (2024). DINOv2: Learning Robust Visual Features without Supervision. Trans. Mach. Learn. Res., Available online: https:\/\/openreview.net\/forum?id=a68SUt6zFt."},{"key":"ref_23","unstructured":"Hendrycks, D., Mazeika, M., and Dietterich, T. (2019, January 6\u20139). Deep Anomaly Detection with Outlier Exposure. Proceedings of the 7th International Conference on Learning Representations (ICLR), New Orleans, LA, USA."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Yu, F., Chen, H., Wang, X., Xian, W., Chen, Y., Liu, F., Madhavan, V., and Darrell, T. (2020, January 14\u201319). BDD100K: A Diverse Driving Dataset for Heterogeneous Multitask Learning. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.00271"},{"key":"ref_25","first-page":"3581","article-title":"Classification with Valid and Adaptive Coverage","volume":"33","author":"Romano","year":"2020","journal-title":"Proc. Adv. Neural Inf. Process. Syst. (NeurIPS)"},{"key":"ref_26","unstructured":"(2018). Road Vehicles\u2014Functional Safety (Standard No. ISO 26262)."},{"key":"ref_27","unstructured":"U.S. Food and Drug Administration (2021). Artificial Intelligence\/Machine Learning (AI\/ML)-Based Software as a Medical Device (SaMD) Action Plan, U.S. Food and Drug Administration."},{"key":"ref_28","unstructured":"European Aviation Safety Agency (2023). Artificial Intelligence Roadmap 2.0: A Human-Centric Approach to AI in Aviation, European Aviation Safety Agency."},{"key":"ref_29","first-page":"2526","article-title":"Conformal Prediction Under Covariate Shift","volume":"32","author":"Tibshirani","year":"2019","journal-title":"Adv. Neural Inf. Process. Syst. (NeurIPS)"},{"key":"ref_30","first-page":"3320","article-title":"How Transferable are Features in Deep Neural Networks?","volume":"27","author":"Yosinski","year":"2014","journal-title":"Proc. Adv. Neural Inf. Process. Syst. (NeurIPS)"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Caesar, H., Bankiti, V., Lang, A.H., Vora, S., Liong, V.E., Xu, Q., Krishnan, A., Pan, Y., Baldan, G., and Beijbom, O. (2020, January 14\u201319). NuScenes: A Multimodal Dataset for Autonomous Driving. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.01164"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/15\/4706\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T10:43:50Z","timestamp":1784889830000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/15\/4706"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,24]]},"references-count":31,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["s26154706"],"URL":"https:\/\/doi.org\/10.3390\/s26154706","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,24]]}}}