CurveBench

CurveBench is the Hard set of CurveBench, a benchmark designed to evaluate the topological reasoning capabilities of large vision-language models (VLMs).
Each sample is a hand-drawn image of disjoint curves paired with the exact rooted-tree structure that encodes the nestedness relationships visible in the image.

Sister dataset: the foundational Easy category (fewer than 6 curves, exhaustive over all rooted trees with up to 6 nodes) lives in AmirMohseni/CurveBench-Easy.

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What is CurveBench?

To the best of our knowledge, CurveBench is the first dataset explicitly designed to benchmark the topological reasoning capabilities of VLMs by mapping visual containment to exact combinatorial structures. While existing datasets often evaluate semantic segmentation or geometric object detection, CurveBench isolates containment and separation as the core signals for visual reasoning.

A model is asked to infer a global topological structure — specifically, a rooted tree where:

• each node represents a contiguous bounded region, and
• each edge denotes the boundary curve that separates two adjacent regions (parent contains child).

The full benchmark contains 756 rigorously hand-drawn images across five categories, split across this dataset and its sister dataset:

Category	Count	Dataset
Easy	300	AmirMohseni/CurveBench-Easy
Polygon	199	this dataset
Topographical	100	this dataset
Maze	100	this dataset
Counting	57	this dataset

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Categories (Hard set)

Polygon (199 images)

Following a systematic construction methodology identical to the Easy category, this subset restricts the geometries entirely to non-intersecting polygons. This tests a model's robustness to sharp angles and piecewise-linear boundaries compared to smooth, continuous Jordan curves.

Topographical (100 images)

Grounded in applied distributions, these images are directly inspired by real-world topographical maps. They mimic the natural behaviour of elevation level sets, bridging the gap between theoretical combinatorial benchmarks and practical visual understanding domains.

Maze (100 images)

Designed to stress-test long-range spatial reasoning, this category features highly convoluted, labyrinthine curves with deep nesting. The spatial entanglement makes distinguishing the interior from the exterior of a boundary visually demanding, forcing models to track complex geometric boundaries over long distances.

Counting (57 images)

This densely populated subset evaluates a model's scalability and capacity limits. Focused primarily on the volume of nested entities, these images are packed with a high number of disjoint curves, challenging the model to construct massive corresponding rooted trees without accumulating structural or logical errors.

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Dataset structure

Splits

Split name	Size	Description
polygon	199	Piecewise-linear polygon boundaries
topographical	100	Topographic-map-inspired curves
maze	100	Labyrinthine, deeply nested curves
counting	57	High-density curve configurations
combined	456	All four categories merged

Fields

Field	Type	Description
image	Image	The hand-drawn image of disjoint curves (PNG)
category	string	One of "Counting", "Maze", "Polygon", "Topographical"
filename	string	Original filename of the image
num_nodes	int32	Number of nodes in the rooted tree (including the implicit root = outer region)
tree	string	Stringified edge list, e.g. "[(0, 1), (0, 2), (1, 3)]" — each tuple is (parent, child) (0 = outermost/root region)

Example row

{
    "image": <PIL.Image>,
    "category": "Counting",
    "filename": "1.PNG",
    "num_nodes": 26,
    "tree": "[(0, 1), (0, 6), (1, 2), (2, 3), (3, 4), (4, 5), (6, 7), ...]",
}

To parse the tree field back to a list of tuples:

import ast

edges = ast.literal_eval(sample["tree"])  # list of (parent, child) int tuples

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Ground truth generation

Ground-truth trees were produced using an automated OpenCV contour-based extraction pipeline that traces the boundary curves in each image and assembles the parent–child containment relationships into a rooted tree. Every annotation was subsequently human-verified to ensure structural correctness.

The extraction scripts are publicly available at:
https://github.com/Amir-Mohseni/CurveBench

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Evaluation

Each predicted tree is compared to the ground truth using tree isomorphism (via NetworkX): a prediction receives full credit only if the predicted edge set is structurally identical to the ground-truth tree up to node relabelling. This provides a deterministic, binary evaluation metric that admits no partial credit for structurally incorrect trees.

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Usage

from datasets import load_dataset

# Load a single category
ds = load_dataset("AmirMohseni/CurveBench", split="polygon")

# Load everything
ds_all = load_dataset("AmirMohseni/CurveBench", split="combined")

# Inspect a sample
sample = ds[0]
print(sample["category"])    # e.g. "Polygon"
print(sample["num_nodes"])   # e.g. 5
print(sample["tree"])        # e.g. "[(0, 1), (1, 2), ...]"
sample["image"].show()       # PIL Image

A ready-made evaluation environment (Prime Intellect Verifiers) is available at amirmohseni/curvebench-env.

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Citation

TO BE ADDED