CircleFlow: Flow-Guided Camera Blur Estimation using a Circle Grid Target

TL;DR

CircleFlow tackles the ill-posed problem of camera PSF estimation by combining a structured circle-grid calibration target with flow-guided, subpixel edge localization. It decouples image and kernel estimation using a binary luminance prior, reconstructs a latent sharp image via optical flow, and models the PSF as an energy-constrained implicit neural representation within a demosaicing-aware joint optimization. The approach yields accurate, spatially varying PSFs that align with ray-traced ground truth and measured SFRs, and it supports effective deblurring using recovered kernels. Practically, CircleFlow enables robust optical characterization and improves restoration pipelines by providing physically consistent, field-dependent blur models. Overall, the method demonstrates strong performance in simulation and real-world calibration, offering a scalable path for integrated optical calibration and computational imaging enhancement.

Abstract

The point spread function (PSF) serves as a fundamental descriptor linking the real-world scene to the captured signal, manifesting as camera blur. Accurate PSF estimation is crucial for both optical characterization and computational vision, yet remains challenging due to the inherent ambiguity and the ill-posed nature of intensity-based deconvolution. We introduce CircleFlow, a high-fidelity PSF estimation framework that employs flow-guided edge localization for precise blur characterization. CircleFlow begins with a structured capture that encodes locally anisotropic and spatially varying PSFs by imaging a circle grid target, while leveraging the target's binary luminance prior to decouple image and kernel estimation. The latent sharp image is then reconstructed through subpixel alignment of an initialized binary structure guided by optical flow, whereas the PSF is modeled as an energy-constrained implicit neural representation. Both components are jointly optimized within a demosaicing-aware differentiable framework, ensuring physically consistent and robust PSF estimation enabled by accurate edge localization. Extensive experiments on simulated and real-world data demonstrate that CircleFlow achieves state-of-the-art accuracy and reliability, validating its effectiveness for practical PSF calibration.

Figures (11)

• Figure 1: Comparison of gradient distributions for a slanted checkerboard and a circle before and after blurring. Hue indicates gradient orientation, and edge width represents blur extent. The checkerboard encodes blur only along two fixed directions, whereas the circle retains a continuous directional field, capturing PSF shape and directional spread more completely.
• Figure 1: Full-field PSF calibration on two imaging systems. From top to bottom: (1) experimental setup example using the Sony $\alpha$6700 with the Tamron 70--300mm lens; (2) full-field PSF calibration results for the Sony $\alpha$6700 + Tamron 70--300mm lens; (3) full-field PSF calibration results for the OnePlus 12 periscope telephoto module, whose PSFs lose their expected field-wise rotational symmetry due to lens-assembly tolerances. CircleFlow consistently captures spatial PSF variations across both interchangeable-lens and mobile imaging systems.
• Figure 2: Construction of the binary proxy $i_0$. Starting from the blurred observation $b$, morphological dilation and erosion are applied independently to suppress blur transitions in dark and bright regions. The resulting precursor is binarized using Otsu’s adaptive thresholding to extract the dark and bright ROIs, whose mean intensities define the characteristic black and white levels of the latent sharp image. Combining these regions yields the binary proxy $i_0$, which preserves the binary luminance pattern and serves as a reliable geometric initialization for subsequent flow-guided refinement.
• Figure 2: PSF estimation under challenging simulation conditions. From left to right: (1) blurred observations, (2) recovered sharp edges overlaid on the ground-truth sharp images, (3) ground-truth PSFs, and (4) estimated PSFs. CircleFlow reconstructs both the latent edge and the PSF with high fidelity.
• Figure 3: Overview of the demosaicing-aware joint optimization framework in CircleFlow. The demosaiced observation $b$ and the binary proxy $i_0$ are concatenated and fed into a flow estimator that predicts a dense, pixel-wise deformation field $V$, yielding the geometrically aligned image $\mathrm{Warp}(i_0,V)$ under the binary luminance prior encoded in $i_0$. In parallel, the PSF $k$ is represented by an implicit neural representation (INR) queried at spatial coordinates $w$ and normalized via softmax, enforcing the PSF’s energy constraint. Both components are optimized jointly within a demosaicing-aware reconstruction loop: the reconstructed sharp image and the estimated PSF are convolved to synthesize a re-blurred image, which is then passed through Bayer sampling and demosaicing to match the observed $b$. This process mitigates interpolation artifacts introduced during demosaicing and enables consistent refinement of geometric alignment and blur modeling for accurate PSF estimation.