CurveBench-Easy

CurveBench-Easy is the foundational split 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 four harder categories (Polygon, Topographical, Maze, Counting) live in AmirMohseni/CurveBench.

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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	this dataset
Polygon	199	AmirMohseni/CurveBench
Topographical	100	AmirMohseni/CurveBench
Maze	100	AmirMohseni/CurveBench
Counting	57	AmirMohseni/CurveBench

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CurveBench-Easy — category description

Easy (300 images): This subset establishes a fundamental baseline, containing spatial configurations with fewer than six curves. To ensure comprehensive coverage of the topological space, all possible rooted tree structures with up to six nodes were enumerated. For each unique combinatorial tree shape, at least two structurally distinct visual representations were manually authored, guaranteeing that models cannot exploit superficial visual similarity.

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Difficulty levels

The Easy set is further divided into three difficulty levels based on structural complexity:

Level	Approx. curve count	Train	Validation	Test	Total
Level 1	fewest curves	84	18	18	120
Level 2	moderate	78	16	18	112
Level 3	most complex	47	10	11	68
Total		210	45	45	300

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Dataset structure

Splits

Split name	Size
level_1_train	84
level_1_validation	18
level_1_test	18
level_2_train	78
level_2_validation	16
level_2_test	18
level_3_train	47
level_3_validation	10
level_3_test	11
total_train	210
total_validation	45
total_test	45

Fields

Field	Type	Description
image	Image	The hand-drawn image of disjoint curves (PNG)
num_nodes	int64	Number of nodes in the rooted tree (including the implicit root = outer region)
tree	List[List[int]]	Edge list of the rooted tree; each element is [parent, child] (0-indexed, 0 = outermost/root region)

Example row

{
    "image": <PIL.Image>,
    "num_nodes": 3,
    "tree": [[0, 1], [1, 2], [2, 3]],
}
# Represents a chain: outer → region 1 → region 2 → region 3

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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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Usage

from datasets import load_dataset

# Load the full training set
ds = load_dataset("AmirMohseni/CurveBench-Easy", split="total_train")

# Load a specific difficulty level
ds_l1 = load_dataset("AmirMohseni/CurveBench-Easy", split="level_1_train")

# Inspect a sample
sample = ds[0]
print(sample["num_nodes"])   # e.g. 3
print(sample["tree"])        # e.g. [[0, 1], [1, 2], [2, 3]]
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