--- title: 'InFlux++: Benchmark for Dynamic Camera Intrinsics' url: https://www.emergentmind.com/topics/influx type: topic --- # InFlux++: Benchmark for Dynamic Camera Intrinsics InFlux++ is a data suite and benchmark for estimating **per-frame camera intrinsics** in videos with **dynamic camera intrinsics**, that is, videos in which the intrinsic parameters vary from frame to frame rather than remaining fixed across a sequence. It was introduced to address two obstacles identified for RGB-based intrinsics prediction: training data is scarce and lacks intrinsics diversity, and existing benchmarks, including the original InFlux, have limited scene and camera motion diversity. InFlux++ therefore combines **InFlux++ Synth**, a large procedurally generated synthetic dataset for training, with **InFlux++ Real**, a large real-world benchmark for evaluation [2607.05389]. ## 1. Definition and problem setting Camera intrinsics determine the mapping from 3D camera coordinates to 2D pixel coordinates. In the pinhole model, \[ \begin{bmatrix} u \\ v \\ 1 \end{bmatrix} = K \begin{bmatrix} X/Z \\ Y/Z \\ 1 \end{bmatrix}, \qquad K = \begin{bmatrix} f_x & 0 & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{bmatrix}. \] The parameters \(f_x\) and \(f_y\) are effective focal lengths in pixels, while \(c_x\) and \(c_y\) are the principal point coordinates. InFlux++ is concerned with the regime in which these quantities, together with distortion parameters in real cameras, are **dynamic** rather than fixed [2607.05389]. The motivating cases are videos in which a zoom lens changes the **lens focal length (LFL)**, the camera changes focus through the **lens-to-object distance (LTO)**, and the lens exhibits **lens breathing**. The thin-lens relation used in the work is \[ \frac{1}{\text{LFL}} = \frac{1}{\text{CFL}} + \frac{1}{\text{LTO}}, \qquad \text{CFL} = \frac{\text{LFL}\cdot\text{LTO}}{\text{LTO} - \text{LFL}}, \] where **CFL** is the effective camera focal length in physical units and is then converted to the pixel focal lengths \(f_x\) and \(f_y\) [2607.05389]. The fixed-intrinsics assumption used by many 3D pipelines is identified as a major limitation. The benchmark is explicitly motivated by the observation that methods such as SfM/SLAM, NeRF, Gaussian Splatting, and monocular depth or pose estimation often assume sequence-wise constant intrinsics, whereas real in-the-wild videos may contain frame-rate zoom and focus variation. A central premise of InFlux++ is therefore that **estimating per-frame intrinsics from RGB images is critical for making 3D methods robust to videos with dynamic intrinsics** [2607.05389]. ## 2. Data suite architecture and camera parameterization InFlux++ has two components with complementary roles: a synthetic training corpus and a real-world benchmark. Their scale and annotation structure are summarized below [2607.05389]. | Component | Scale | Core content | |---|---:|---| | InFlux++ Synth | 1,841 videos, 441,840 frames | RGB, per-frame intrinsics \(K\), pose, LFL, LTO, CFL; subset with depth and normals | | InFlux++ Real | 334 videos, 514K+ frames | RGB with per-frame calibrated intrinsics from lens metadata and LUTs | In the synthetic component, **LFL** and **LTO** are the primary time-varying physical parameters. The paper states that temporal variation in these quantities produces physically plausible variation in **CFL**, together with **lens breathing**, even when LFL is fixed. Synthetic distortion is added through a Brown–Conrady model. For a normalized point \(\mathbf{x}=(x,y)\) with \(r=\|\mathbf{x}\|\), the radial model is \[ \mathbf{x}_d = \mathbf{x}\left(1+k_1 r^2 + k_2 r^4\right), \] with optional tangential parameters \(p_1,p_2\). The corresponding radial displacement in normalized coordinates is \[ \Delta r = r(k_1 r^2 + k_2 r^4), \] and in pixels, \[ \Delta \mathrm{pxl}(r) = \mathrm{CFL}(k_1 r^3 + k_2 r^5). \] The coefficients \(k_1\) and \(k_2\) are obtained by sampling desired pixel displacements at two edge control points and solving a \(2\times2\) system, while \(p_1,p_2\) may be sampled from \(\mathcal{N}(0,10^{-4})\) [2607.05389]. This parameterization reflects a deliberate modeling choice. The work does not treat dynamic intrinsics merely as dynamic field of view; it represents them as a coupled consequence of zoom, focus, distortion, and defocus blur. A plausible implication is that InFlux++ is intended not only as a benchmark for focal-length regression, but also as an optical-model benchmark in which peripheral rays, distortion, and focus-dependent image formation are part of the supervision signal [2607.05389]. ## 3. InFlux++ Synth InFlux++ Synth is described as a **large-scale procedurally generated synthetic video dataset with 441K+ annotated frames from 1841 high-resolution videos**. In the detailed dataset statistics, this becomes **1,841 videos** and **441,840 frames**, with **10 s per video at 24 FPS** and resolution \(1280\times720\). The dataset is divided into **1,040 indoor videos (249,600 frames)** and **801 nature videos (192,240 frames)** [2607.05389]. All videos provide per-frame **RGB**, intrinsics matrix \(K\), camera pose \(T\), **LFL**, **LTO**, and **CFL**. A subset of **818 videos (196,320 frames)** additionally includes **depth maps (blurred + pinhole)** and **surface normals (blurred + pinhole)**. Scene diversity includes indoor categories such as living rooms, bedrooms, bathrooms, kitchens, and offices, and nature categories such as forests, deserts, caves, mountains, coasts, arctic, and underwater. The scenes also include **dynamic objects**, including animals, falling leaves, and water, as well as **non-Lambertian materials, reflections, and mirrors** [2607.05389]. The rendering stack is built on **Infinigen** and **Infinigen Indoors**, with photorealistic rendering through **Blender’s Cycles** engine. Camera trajectories are produced through Infinigen’s **Rapidly-Exploring Random Tree (RRT)** planner, which samples collision-free positional waypoints and connects them with Bézier-interpolated camera poses. Additional filtering rejects views with too much sky or geometry that is too close, and applies a **dominant surface normal** check: a single large planar patch is considered dominant if it covers more than **65% of samples indoors** or more than **80% in nature**. Local replanning is used when orientation sampling fails at a waypoint, and free-space checks prevent the camera from passing through geometry [2607.05389]. The temporal dynamics of intrinsics are generated by bounded random walks. For **LFL**, keyframes follow \[ x_{t+1}=x_t+\Delta x, \] with \(\Delta x\sim\mathrm{Uniform}(-\delta_{\max},\delta_{\max})\), clipped to \([8\text{mm},100\text{mm}]\), and smoothly interpolated with Bézier curves. For **LTO**, the paper notes that direct random walks tend to produce frames where everything is out of focus, so focus depth is instead parameterized by \[ d_{\text{focus}} = d_{\text{near}} + (d_{\text{far}} - d_{\text{near}})\alpha, \] where \(\alpha\in[0,1]\) follows a bounded random walk, and \(d_{\text{near}}, d_{\text{far}}\) are estimated by ray tracing using 5th and 95th percentile visible depths from 1000 sampled rays. This ensures that portions of the scene remain in focus throughout the sequence [2607.05389]. The synthetic loader is itself part of the contribution. It adds on-the-fly **radial distortion**, optional tangential distortion, photometric augmentations such as gamma, tone curve, color jitter, noise, and JPEG artifacts, and geometric augmentations such as aspect ratio changes and cropping. The augmentations explicitly **disable blur, sharpen, and downscale** so as not to interfere with thin-lens blur cues. This suggests that InFlux++ Synth is designed as a training environment in which optical effects relevant to calibration are preserved rather than randomized away [2607.05389]. ## 4. InFlux++ Real InFlux++ Real is the benchmark component. It is described as a **large-scale real-world benchmark that extends InFlux with 514K+ newly captured frames across 334 high-resolution videos**, and in the detailed statistics as **334 videos**, **514,000+ frames**, resolution \(3424\times2202\), and **23.976 FPS** [2607.05389]. The hardware platform consists of an **ARRI Alexa Mini** with two cinema zoom lenses: **Canon CINE-SERVO 17–120 mm (canon17)** and **Fujinon Premista 80–250 mm (premista80)**. These lenses provide **/i Technology metadata**, specifically per-frame **lens focal length (LFL)** and **focus distance (FD)**. Ground-truth intrinsics, including distortion, are obtained from **per-lens lookup tables (LUTs)** that map \((\mathrm{LFL},\mathrm{FD})\) to intrinsics. The LUTs are constructed from calibration board captures at a grid of LFL and FD settings, followed by interpolation [2607.05389]. A major methodological change relative to the original InFlux is the introduction of a **camera-moving board-based calibration** for large field-spatial-footprint calibration. The calibration pattern consists of large AprilTag arrays on a rigid screen of approximately \(5.45\text{m}\times3.06\text{m}\), installed in a multi-story lecture hall with balcony. The board is fixed while the camera is moved and rotated from multiple positions, including ground floor left and right, balcony left and right, and additional ground positions for shorter FD. According to the paper, this configuration excites all rotational axes, covers the entire field spatial footprint, and avoids the complexity and instability of drone-based calibration [2607.05389]. The benchmark is also intended to broaden evaluation coverage. Compared with the original InFlux, InFlux++ Real includes more **urban** scenes, more **everyday/domestic** indoor scenes, **sports and recreation**, **moving vehicle** captures, and **elevated viewpoints**. The parallax statistics are explicitly reported: the original InFlux contains **324 low**, **35 medium**, and **27 high parallax** videos, whereas InFlux++ Real contains **119 low**, **28 medium**, and **183 high-parallax** videos. The repaired **canon17** lens is additionally reported to have a significant principal point offset, which broadens the range of \(c_x,c_y\) values [2607.05389]. Privacy protection is built into the release. Frames are processed with **RetinaFace** for face detection and **EgoBlur** for license plates, using full-image and \(3\times3\) tile inference, confidence thresholding, and non-maximum suppression; detected regions are then blurred. This places the benchmark in the category of calibration datasets intended for public dissemination rather than only internal evaluation [2607.05389]. ## 5. Evaluation protocol and baseline methods The benchmark evaluates predictions using parameter-error recalls and reprojection-style endpoint error. For focal lengths and principal points, percent error is defined per frame as \[ \mathrm{PE}(f_x)=\frac{|f_x^{\mathrm{pred}}-f_x^{\mathrm{gt}}|}{f_x^{\mathrm{gt}}}\cdot100\%, \] with analogous quantities for \(f_y,c_x,c_y\). Reported recalls are **Recall@\{1\%,10\%,20\%\}** for \(f_x,f_y\) and **Recall@\{0.5\%,1\%,2\%\}** for \(c_x,c_y\) [2607.05389]. The endpoint error (EPE) metric is defined by projecting visible 3D points with ground-truth and predicted intrinsics, including distortion, and computing the Euclidean image-plane displacement \[ \mathrm{EPE}(\mathbf{P})=\left\|\mathbf{u}^{\mathrm{gt}}-\mathbf{u}^{\mathrm{pred}}\right\|_2. \] InFlux++ modifies the visibility filtering used for Brown–Conrady distortion. The distorted radial mapping \[ r_d(r)=r(1+k_1 r^2+k_2 r^4) \] is required to remain on its monotonic branch, with cutoff radius \(r_*\) given by the first positive root of \[ r_d'(r)=1+3k_1 r^2+5k_2 r^4=0. \] A point is only considered visible if its distorted projection lies in image bounds and its undistorted radius satisfies \(r