Autoregressive High-Order Finite Difference Modulo Imaging: High-Dynamic Range for Computer Vision Applications

TL;DR

This work addresses HDR reconstruction from modulo imaging by reframing Unlimited Sampling Framework recovery as an autoregressive high-order finite-difference phase-unwrapping problem in 2D. It introduces AHFD, which combines neighborhood vectorization, a $DCT$-domain autoregressive solver, and a stride-artifact removal step to enable robust HDR reconstruction from modulo measurements. The method achieves competitive HDR restoration compared with state-of-the-art optimization and deep-learning approaches and improves object-detection performance in autonomous-driving scenarios without retraining. These contributions advance practical HDR sensing with modulo-ADC hardware, enabling better handling of saturated scenes in real-time vision tasks.

Abstract

High dynamic range (HDR) imaging is vital for capturing the full range of light tones in scenes, essential for computer vision tasks such as autonomous driving. Standard commercial imaging systems face limitations in capacity for well depth, and quantization precision, hindering their HDR capabilities. Modulo imaging, based on unlimited sampling (US) theory, addresses these limitations by using a modulo analog-to-digital approach that resets signals upon saturation, enabling estimation of pixel resets through neighboring pixel intensities. Despite the effectiveness of (US) algorithms in one-dimensional signals, their optimization problem for two-dimensional signals remains unclear. This work formulates the US framework as an autoregressive $\ell_2$ phase unwrapping problem, providing computationally efficient solutions in the discrete cosine domain jointly with a stride removal algorithm also based on spatial differences. By leveraging higher-order finite differences for two-dimensional images, our approach enhances HDR image reconstruction from modulo images, demonstrating its efficacy in improving object detection in autonomous driving scenes without retraining.

Figures (6)

• Figure 1: Visual representation of Itoh's condition. For a given band-limited signal, the bounded threshold for the second finite difference its reduced, enabling the unwrapping of modulo samples in contrast to use the first finite difference. Figure inspired from bhandari2020unlimited.
• Figure 2: Proposed AHFD method for HDR image restoration from modulo measurements composed of three components: 1) Autoregressive phaseunwrapping algorithm, and 2) Stripe Artifact Removal, 3) The operator $\textbf{P}\texttt{vec}$ to adapt AHFD for matrices.
• Figure 3: Pixel neighborhood vectorization. a) Reference image, b) column vectorization order using the $\text{vec}(\cdot)$ operator, c-d) proposed pixel neighborhood vectorization $\textbf{P}\text{vec}(\cdot)$ which follows either a vertical or horizontal trajectory. Column vectorization creates artificial discontinuities at the end of each column, whereas our strategy maintains a next-pixel vectorization path.
• Figure 4: Artifacts from various image unwrapping algorithms. In Undmodnet zhou2020unmodnet, over-estimating unwrapping levels results in "stains" in the images. SPUD pineda2020spud when failure to maintain Itoh's condition causes "light leaks" around synthetic wraps at the image borders. Alternatively, USF bhandari2020unlimited artifacts produce structural lines that overlap with correctly unwrapped images, often referred to as "stripes" in remote sensing images.
• Figure 5: Comparison with state-of-the-art recovery methods from the modulo images. (a-b) correspond to saturated and modulo measurements under different intensity levels, respectively. (c-f) Corresponding to different recovery methods and the proposed Ours-h method, finally, (g) corresponds to the ground truth image.