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Janne Heikkilä

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Computer Vision math.NA Symbolic Computation

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preprint2026arXiv

Differentiable Ray Tracing with Gaussians for Unified Radio Propagation Simulation and View Synthesis

Explicit neural representations such as 3D Gaussian Splatting (3DGS) enable high-fidelity and real-time novel view synthesis, yet optimize for alpha-composited optical appearance rather than ray-intersectable geometry. In contrast, radio-frequency (RF) digital twins require deterministic multi-bounce paths, where the geometry dictates trajectories and their associated attenuation and delay. We introduce a framework enabling differentiable RF propagation simulation directly within visually reconstructed neural scenes, allowing point-to-point path computation between arbitrary 3D locations while preserving high-quality visual rendering. Unlike conventional RF simulation pipelines that rely on manually constructed meshes, we embed Gaussian primitives into a hardware-accelerated ray tracing structure as the underlying spatial representation. By extracting physically meaningful channel impulse responses from visual-only reconstructions, we provide cross-modal evidence that neural reconstructions can serve as unified spatial representations for both electromagnetic propagation simulation and photorealistic view synthesis.

preprint2026arXiv

OP2GS: Object-Aware 3D Gaussian Splatting with Dual-Opacity Primitives

3D Gaussian Splatting (3DGS) provides an explicit and efficient scene representation, but its primitives lack inherent object-level identity, hindering downstream tasks such as open-vocabulary scene understanding. Existing methods typically address this by either distilling high-dimensional feature embeddings into Gaussians or by lifting 2D mask labels into 3D via heuristic refinement. However, feature-based approaches incur heavy storage and decoding overhead, while lifting-based pipelines remain vulnerable to label contamination: Gaussians necessary for appearance reconstruction often receive incorrect object labels during 2D-to-3D projection. We propose OP2GS, an object-aware Gaussian representation that augments each primitive with an explicit instance identity and a dedicated instance opacity $σ^{*}$ for object-mask rendering. The original opacity $σ$ remains responsible for visual reconstruction, while $σ^{*}$ models whether a Gaussian should contribute to a particular object mask. This dual-opacity formulation decouples visual existence from instance occupancy: mislabeled Gaussians can remain available for image rendering while becoming transparent in the object-mask branch. To learn this representation, we introduce a random object loss that optimizes the 1D instance occupancy field using the standard transmittance-based visibility of 3DGS. Semantic descriptors are then attached at the object level through multi-view aggregation, eliminating per-Gaussian feature storage. Compared with feature-training approaches, OP2GS achieves competitive open-vocabulary performance while significantly reducing computational overhead. Compared with training-free pipelines, it leverages physically consistent occupancy learning to resolve visibility ambiguities.

preprint2026arXiv

Solving Minimal Problems Without Matrix Inversion Using FFT-Based Interpolation

Estimating camera geometry typically involves solving minimal problems formulated as systems of multivariate polynomial equations, which often pose computational challenges when using existing Gröbner-basis or resultant-based methods due to matrix inversion needed in the online solver. Here we propose a sampling-based, matrix inversion-free method that constructs the solvers using sparse hidden-variable resultants. The determinant polynomial in the hidden variable is efficiently reconstructed via inverse fast Fourier transform interpolation from sampled evaluations, avoiding symbolic expansion. Solving this polynomial yields the hidden variable, and the remaining unknowns are recovered by identifying rank-1 deficient submatrices and applying Cramer's rule. A greatest common divisor-based criterion ensures robust submatrix identification under noise. Experiments on diverse minimal problems demonstrate that the proposed solver achieves strong numerical stability and competitive runtime, particularly for small-scale problems, providing a practical alternative to traditional Gröbner-basis and resultant-based solvers.

preprint2023arXiv

BS3D: Building-scale 3D Reconstruction from RGB-D Images

Various datasets have been proposed for simultaneous localization and mapping (SLAM) and related problems. Existing datasets often include small environments, have incomplete ground truth, or lack important sensor data, such as depth and infrared images. We propose an easy-to-use framework for acquiring building-scale 3D reconstruction using a consumer depth camera. Unlike complex and expensive acquisition setups, our system enables crowd-sourcing, which can greatly benefit data-hungry algorithms. Compared to similar systems, we utilize raw depth maps for odometry computation and loop closure refinement which results in better reconstructions. We acquire a building-scale 3D dataset (BS3D) and demonstrate its value by training an improved monocular depth estimation model. As a unique experiment, we benchmark visual-inertial odometry methods using both color and active infrared images.

preprint2022arXiv

Optimal Correction Cost for Object Detection Evaluation

Mean Average Precision (mAP) is the primary evaluation measure for object detection. Although object detection has a broad range of applications, mAP evaluates detectors in terms of the performance of ranked instance retrieval. Such the assumption for the evaluation task does not suit some downstream tasks. To alleviate the gap between downstream tasks and the evaluation scenario, we propose Optimal Correction Cost (OC-cost), which assesses detection accuracy at image level. OC-cost computes the cost of correcting detections to ground truths as a measure of accuracy. The cost is obtained by solving an optimal transportation problem between the detections and the ground truths. Unlike mAP, OC-cost is designed to penalize false positive and false negative detections properly, and every image in a dataset is treated equally. Our experimental result validates that OC-cost has better agreement with human preference than a ranking-based measure, i.e., mAP for a single image. We also show that detectors' rankings by OC-cost are more consistent on different data splits than mAP. Our goal is not to replace mAP with OC-cost but provide an additional tool to evaluate detectors from another aspect. To help future researchers and developers choose a target measure, we provide a series of experiments to clarify how mAP and OC-cost differ.

preprint2022arXiv

OVE6D: Object Viewpoint Encoding for Depth-based 6D Object Pose Estimation

This paper proposes a universal framework, called OVE6D, for model-based 6D object pose estimation from a single depth image and a target object mask. Our model is trained using purely synthetic data rendered from ShapeNet, and, unlike most of the existing methods, it generalizes well on new real-world objects without any fine-tuning. We achieve this by decomposing the 6D pose into viewpoint, in-plane rotation around the camera optical axis and translation, and introducing novel lightweight modules for estimating each component in a cascaded manner. The resulting network contains less than 4M parameters while demonstrating excellent performance on the challenging T-LESS and Occluded LINEMOD datasets without any dataset-specific training. We show that OVE6D outperforms some contemporary deep learning-based pose estimation methods specifically trained for individual objects or datasets with real-world training data. The implementation and the pre-trained model will be made publicly available.

preprint2020arXiv

Computing stable resultant-based minimal solvers by hiding a variable

Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e., solving minimal problems, in a RANSAC-style framework. Minimal problems often result in complex systems of polynomial equations. The existing state-of-the-art methods for solving such systems are either based on Gröbner bases and the action matrix method, which have been extensively studied and optimized in the recent years or recently proposed approach based on a sparse resultant computation using an extra variable. In this paper, we study an interesting alternative sparse resultant-based method for solving sparse systems of polynomial equations by hiding one variable. This approach results in a larger eigenvalue problem than the action matrix and extra variable sparse resultant-based methods; however, it does not need to compute an inverse or elimination of large matrices that may be numerically unstable. The proposed approach includes several improvements to the standard sparse resultant algorithms, which significantly improves the efficiency and stability of the hidden variable resultant-based solvers as we demonstrate on several interesting computer vision problems. We show that for the studied problems, our sparse resultant based approach leads to more stable solvers than the state-of-the-art Gröbner bases-based solvers as well as existing sparse resultant-based solvers, especially in close to critical configurations. Our new method can be fully automated and incorporated into existing tools for the automatic generation of efficient minimal solvers.

preprint2020arXiv

Improving land cover segmentation across satellites using domain adaptation

Land use and land cover mapping are essential to various fields of study, including forestry, agriculture, and urban management. Using earth observation satellites both facilitate and accelerate the task. Lately, deep learning methods have proven to be excellent at automating the mapping via semantic image segmentation. However, because deep neural networks require large amounts of labeled data, it is not easy to exploit the full potential of satellite imagery. Additionally, the land cover tends to differ in appearance from one region to another; therefore, having labeled data from one location does not necessarily help in mapping others. Furthermore, satellite images come in various multispectral bands (the bands could range from RGB to over twelve bands). In this paper, we aim at using domain adaptation to solve the aforementioned problems. We applied a well-performing domain adaptation approach on datasets we have built using RGB images from Sentinel-2, WorldView-2, and Pleiades-1 satellites with Corine Land Cover as ground-truth labels. We have also used the DeepGlobe land cover dataset. Experiments show a significant improvement over results obtained without the use of domain adaptation. In some cases, an improvement of over 20% MIoU. At times it even manages to correct errors in the ground-truth labels.

preprint2020arXiv

Learning non-rigid surface reconstruction from spatio-temporal image patches

We present a method to reconstruct a dense spatio-temporal depth map of a non-rigidly deformable object directly from a video sequence. The estimation of depth is performed locally on spatio-temporal patches of the video, and then the full depth video of the entire shape is recovered by combining them together. Since the geometric complexity of a local spatio-temporal patch of a deforming non-rigid object is often simple enough to be faithfully represented with a parametric model, we artificially generate a database of small deforming rectangular meshes rendered with different material properties and light conditions, along with their corresponding depth videos, and use such data to train a convolutional neural network. We tested our method on both synthetic and Kinect data and experimentally observed that the reconstruction error is significantly lower than the one obtained using other approaches like conventional non-rigid structure from motion.

preprint2020arXiv

LSD$_2$ -- Joint Denoising and Deblurring of Short and Long Exposure Images with CNNs

The paper addresses the problem of acquiring high-quality photographs with handheld smartphone cameras in low-light imaging conditions. We propose an approach based on capturing pairs of short and long exposure images in rapid succession and fusing them into a single high-quality photograph. Unlike existing methods, we take advantage of both images simultaneously and perform a joint denoising and deblurring using a convolutional neural network. A novel approach is introduced to generate realistic short-long exposure image pairs. The method produces good images in extremely challenging conditions and outperforms existing denoising and deblurring methods. It also enables exposure fusion in the presence of motion blur.

preprint2016arXiv

Learning Joint Representations of Videos and Sentences with Web Image Search

Our objective is video retrieval based on natural language queries. In addition, we consider the analogous problem of retrieving sentences or generating descriptions given an input video. Recent work has addressed the problem by embedding visual and textual inputs into a common space where semantic similarities correlate to distances. We also adopt the embedding approach, and make the following contributions: First, we utilize web image search in sentence embedding process to disambiguate fine-grained visual concepts. Second, we propose embedding models for sentence, image, and video inputs whose parameters are learned simultaneously. Finally, we show how the proposed model can be applied to description generation. Overall, we observe a clear improvement over the state-of-the-art methods in the video and sentence retrieval tasks. In description generation, the performance level is comparable to the current state-of-the-art, although our embeddings were trained for the retrieval tasks.

preprint2016arXiv

Video Summarization using Deep Semantic Features

This paper presents a video summarization technique for an Internet video to provide a quick way to overview its content. This is a challenging problem because finding important or informative parts of the original video requires to understand its content. Furthermore the content of Internet videos is very diverse, ranging from home videos to documentaries, which makes video summarization much more tough as prior knowledge is almost not available. To tackle this problem, we propose to use deep video features that can encode various levels of content semantics, including objects, actions, and scenes, improving the efficiency of standard video summarization techniques. For this, we design a deep neural network that maps videos as well as descriptions to a common semantic space and jointly trained it with associated pairs of videos and descriptions. To generate a video summary, we extract the deep features from each segment of the original video and apply a clustering-based summarization technique to them. We evaluate our video summaries using the SumMe dataset as well as baseline approaches. The results demonstrated the advantages of incorporating our deep semantic features in a video summarization technique.

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