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Slow Perception: Let's Perceive Geometric Figures Step-by-step
Haoran Wei, Youyang Yin, Yumeng Li, Jia Wang, Liang Zhao, Jianjian Sun, Zheng Ge, Xiangyu Zhang, Daxin Jiang
TL;DR
Geometric parsing is challenging because visual units have spatial dependencies, while independently predicted components can disagree on shared coordinates. Slow perception decomposes figures into basic units and traces lines through short steps; the authors report a 6% F1-score improvement and propose it as a potentially useful direction beyond geometry parsing.
Problem
Independent predictions of geometric components can yield inconsistent coordinates for shared points, making geometric parsing difficult despite its academic and applied value.
Source: §1 · pp. 1–2Method
Slow perception decomposes figures into basic units and traces each line through intermediate gaze points bounded by a perceptual ruler.
Source: §1 · p. 2Results
Slow perception improves the F1-score by 6%.
Source: §1 · p. 2Takeaways & Limitations
The authors conclude that slow perception is effective for geometric parsing and may inspire work in other general vision areas.
Source: §5 · p. 8The multistroke perception-flow method is applied only to lines; circles and curves are left for future work.
Source: §3.3 · p. 5
Abstract
from arXiv · showhide
Recently, "visual o1" began to enter people's vision, with expectations that this slow-thinking design can solve visual reasoning tasks, especially geometric math problems. However, the reality is that current LVLMs (Large Vision Language Models) can hardly even accurately copy a geometric figure, let alone truly understand the complex inherent logic and spatial relationships within geometric shapes. We believe accurate copying (strong perception) is the first step to visual o1. Accordingly, we introduce the concept of "slow perception" (SP), which guides the model to gradually perceive basic point-line combinations, as our humans, reconstruct complex geometric structures progressively. There are two-fold stages in SP: a) perception decomposition. Perception is not instantaneous. In this stage, complex geometric figures are broken down into basic simple units to unify geometry representation. b) perception flow, which acknowledges that accurately tracing a line is not an easy task. This stage aims to avoid "long visual jumps" in regressing line segments by using a proposed "perceptual ruler" to trace each line stroke-by-stroke. Surprisingly, such a human-like perception manner enjoys an inference time scaling law -- the slower, the better. Researchers strive to speed up the model's perception in the past, but we slow it down again, allowing the model to read the image step-by-step and carefully.
1. Introduction
The introduction frames geometric parsing as important but difficult because geometric units have spatial dependencies, and existing detection can produce inconsistent shared coordinates. It proposes slow perception, which decomposes figures into units and traces lines in stages; the authors report a 6% F1-score improvement.
1. Introduction
- Independent detection of geometric components can give inconsistent coordinates for a shared vertex, making traditional detection struggle with geometric parsing.For example, separately predicted sides AB and BC may disagree on point B.Source: §1 · p. 2
- The authors motivate slow perception by comparing it to manually breaking a complex figure into small units and drawing each part stroke-by-stroke.This is presented as their answer to where current LVLM modeling paradigms fall short.Source: §1 · p. 2
- Slow perception decomposes shapes into basic visual units, then traces each line through successive gaze points from its start to endpoint.The number of gaze points depends on line length and the preset perceptual ruler.Source: Figure 1 · p. 1, §1 · p. 2
- The paper contributes a rendering method and a dataset of 200,000 synthetic samples plus 480 manually annotated real-world figures.The real-world figures are split into 120 validation and 360 test examples.Source: §1 · p. 2
- 6% F1-score improvement is reported for slow perception in geometric parsing.The passage does not specify a baseline or evaluation condition for this headline figure.Source: §1 · p. 2
- The authors argue that geometric parsing findings may offer insights for other computer-vision research areas.They frame geometric figures as abstractions of natural visual objects.Source: §1 · p. 2
2. Related Works
The related-work discussion contrasts geometry's shared-point dependencies with independently predicted detections, and questions whether faster perception is always preferable. It also notes concerns that LVLMs may read images superficially, missing details, logic, and spatial relationships.
2.1. Object Detection as Vision Perception
- Figure 3's LVLM framework uses serialized point prediction, allowing later points to reference earlier coordinates, while a perceptual ruler caps each prediction step.The caption describes the approach as adaptable to popular LVLM frameworks.Source: Figure 3 · p. 3
- Independent detection of geometric components cannot ensure closure or consistent shared-point coordinates, prompting the question of whether faster perception is always better.The discussion places this concern against a trend from two-stage detection toward increasingly fast one-stage methods.Source: §2.1 · pp. 2–3
2.2. LVLM for Vision Perception
- LVLMs commonly use an encoder-perceiver-decoder architecture and training with pretraining followed by supervised fine-tuning.The passage notes that these frameworks have become convergent.Source: §2.2 · p. 3
- Prior work is described as finding that LVLMs may read images superficially, making details, logic, and spatial relationships difficult to capture.The discussion also notes attempts to enhance VLM capabilities with chain of thought.Source: §2.2 · p. 3
3. Methodology
The methodology combines an LVLM parsing setup and synthetic-data engine with slow perception’s decomposition and local-to-whole line tracing. It trains on generated geometry and evaluates parsed line segments using averaged horizontal and vertical IoU.
3.1. Architecture
- The experiments use GOT-OCR2.0 as the primary LVLM and Qwen2-VL and Vary to further test slow perception.The architecture pairs a vision encoder and LLM decoder with a linear channel-mapping layer.Source: §3.1 · p. 3
3.2. Data Engine
- The data engine renders 200k synthetic images from quadrilateral bases, varying points and optionally adding circles and vertex labels.It varies line thickness, style, and resolution; 150k images use randomly selected DPI values from 36 to 300, and 50k use 96 DPI.Source: §3.2 · pp. 3–4
- Coordinate labels are converted through pixel coordinates and normalized to unify training data with manually annotated validation and test data.The benchmark contains 480 middle-school exam figures: 120 validation images and 360 test images.Source: §3.2 · p. 4
- The rendered training lines have lengths mainly between 2 and 10, informing the perceptual-ruler settings.Figure 4 shows line-length and angle distributions.Source: §3.2 · p. 4, Figure 4 · p. 4
3.3. Slow Perception
- Perception decomposition represents complex figures line-by-line, providing a unified representation that can avoid multiple peaks in nested shapes.This first slow-down stage decomposes figures into basic units rather than modeling them as closed polygons.Source: §3.3 · p. 4
- Perception flow traces lines through sub-lines no longer than ruler length d; smaller d requires more strokes and increases computation and inference time.The multistroke procedure is applied to lines, while other shapes such as circles and curves are left for future work.Source: §3.3 · p. 5
3.4. Optimization and Evaluation Objectives
- Training maps geometry images to parsing text sequences, and evaluation classifies predicted line segments using the average of horizontal and vertical IoU.Figure 5 shows a rendered sample and its text labels with ruler length 4; no prompts are used.Source: §3.4 · p. 5, Figure 5 · p. 5
4. Experiment
Experiments find that slow perception improves geometric parsing, with performance rising as the perceptual ruler shortens and inference takes longer. Tests across validation data, other LVLMs, encoder settings, gaze-point jitter, and visualizations examine the method’s robustness and operation.
4.1. Experimental Settings
- Experiments use SP-1, three LVLMs, and F1-score, precision, and recall, with an infinite ruler defining the no-slow-perception baseline.SP-1 contains 200,000 synthetic training pairs and 480 real-scenario evaluation samples, split into 120 validation and 360 test images.Source: §4.1 · pp. 5–7
4.2. Main Results
- At ruler length 4, slow perception improves F1-score by 6.1% over the baseline at 0.75 IoU on the SP-1 test set.The result is reported for GOT-OCR2.0; Table 1 distinguishes short and long segments and reports results at 0.75 and 0.9 IoU.Source: Table 1 · p. 6, §4.2 · p. 7
- The SP-1 validation results show stable gains, although improvements are lower than on the test set, whose longer lines are easier to predict.The validation figures contain more interwoven short lines, which are more challenging to predict.Source: Table 2 · p. 6, §4.2 · p. 7
- Shorter perceptual rulers improve almost all metrics while increasing the number of strokes, intermediate gaze points, computational cost, and inference time.The authors describe this trend as an inference-time scaling law to some extent.Source: Figure 6 · p. 7
4.3. Ablation Study
- Slow perception yields about a 2% performance increase on Qwen2-VL and Vary-toy, while unfreezing GOT’s vision encoder improves the baseline and enlarges the slow-perception gain.The auxiliary models were trained with frozen encoders; the encoder comparison tests GOT with its vision encoder frozen or unfrozen.Source: §4.3 · pp. 7–8, Table 3 · p. 7, Table 4 · p. 7
- Jittering gaze-point annotations by up to one-tenth of a line’s length reduces performance by less than 1%, while slow perception remains above baseline on F1-score (56.6% vs. 51.4%).The results suggest the gradual start-to-end perception flow may matter more than precise intermediate gaze points.Source: §4.3 · p. 8, Table 5 · p. 8
4.4. Visualization Result
- Visualizations show the model drawing each line from its start to end through multiple strokes, with an apparent gradual correction process.Figure 8 presents the input image, stroke trace route, and final parsing result.Source: Figure 8 · p. 8, §4.4 · p. 8
5. Conclusion
The conclusion frames accurate geometric perception as a prerequisite for visual reasoning and proposes slow perception for geometric parsing. The reported results support its effectiveness for this task, and the authors suggest it may inspire approaches in other vision areas.
5. Conclusion
- Slow perception is proposed for geometric parsing, and the authors report that it is effective.They frame accurate copying of visual geometry as a first step toward visual o1.Source: §5 · p. 8
- The authors argue that models should solve the fundamental perception task before being expected to answer complex visual reasoning questions.The conclusion specifically raises geometry mathematics as an example of such reasoning.Source: §5 · p. 8
- The authors suggest slow perception may also be inspiring for other general vision areas.They describe geometric figures as abstractions of natural visual scenes.Source: §5 · p. 8
6. Appendix
The appendix explores downstream uses of slow perception, including geometry parsing as a reference for question answering, visual comparisons with other models, and possible extensions to broader tasks.
6. Appendix
- Real geometric images differ from rendered training data, so the authors post-trained with in-house real data; they frame this as exploration that does not affect the main-body conclusions.The appendix also presents downstream usage skills for slow perception.Source: §6 · p. 9
6.1. More Complete Geometric Shapes
- Adding point and line labels for downstream applications requires key-value pairs in the ground truth, a feature the authors say is simple within their LVLM framework.Figure 9 presents label addition as separate from slow perception itself.Source: §6.1 · p. 9, Figure 9 · p. 9
6.2. From Geometric Parsing to Reasoning
- 60.10% accuracy, up from 53.37% (+6.73%), when GPT-4o received geometric parsing results as a reference on Mathvista’s Geo subset.The authors note that parsing beforehand and providing text is not the optimal approach; they point to repeated image reading and timely auxiliary-line drawing as a more human-like direction.Source: Table 6 · p. 9, §6.2 · p. 9
6.3. Visualization Results Comparison
- GPT-4o and Claude-3.5 produce unsatisfactory fine-grained parses; the one-order baseline is closer to the input but has wrong lines, while full slow perception performs better.The comparison uses TikZ outputs from the two LVLMs and renders them for visual inspection.Source: §6.3 · p. 10
6.4. Future Outlook
- The authors propose scaling perceptual computation with target difficulty and plan to explore reinforcement learning with a variable-length perceptual ruler and applications beyond geometry parsing.They compare the future goal to handling occluded versus non-occluded objects in detection.Source: §6.4 · p. 10