arXiv:2512.05539cs.CVmath.ST2025-12

提出可精确分割小图像块的贝叶斯理想观察者,融合几何与像素信息。

Ideal Observer for Segmentation of Dead Leaves Images

  • 基于几何先验与似然建模,构建贝叶斯理想分割框架
  • 在108个数据集上验证,理想观察者性能优于其他模型
  • 适用于小像素集分析,为人类与算法提供性能上限参考

场景可见部分由重叠表面间的遮挡决定。本文研究‘死叶’模型,通过独立采样位置、形状、颜色和纹理的物体(‘叶子’)并叠加至覆盖图像为止来模拟。在此基础上,我们提出一个自包含框架,严格定义死叶模型,并推导出有限像素集的解析贝叶斯理想观察者。论文重点在于先验概率的推导,使观察者超越仅依赖像素相似性的方法,引入几何信息。该计算仅对小像素集(最多9-10像素)可行。通过逐步推导、可视化和实例展示增强可读性。我们在108个不同纹理强度、叶尺寸和图像大小的死叶图像数据集上,实证评估了三种可计算观察者(仅先验、仅似然、完整理想观察者)及随机基线。似然仅模型性能随纹理强度和图像增大而下降;先验仅模型性能随叶尺寸减小和最大图像维度增大而下降。所有模型基观察者均显著优于随机基线,理想观察者因结合双源信息始终最优。该模型为小像素集分割提供了原理性性能上限,可用于与人类观察者及算法比较。

原文摘要 · Abstract (English)

The visible parts of a scene are determined by occlusion among overlapping surfaces. Here we consider "dead leaves" models, which replicate this by independently sampling objects ("leaves") with position, shape, color, and texture and layering them until the image is covered. Building on prior theory, we present a self-contained framework that rigorously defines the dead leaves model and derives an analytical Bayesian ideal observer for partitioning finite pixel sets. The longest part of the paper spans the derivation of the prior probability, which elevates the observer beyond pixel-similarity methods by incorporating geometric information. These computations are practical only for small pixel sets (up to 9-10 pixels). We emphasize accessibility through step-by-step derivations, extensive visualizations, and examples. We empirically evaluate three tractable observers (prior-only, likelihood-only, and the full ideal observer), plus a random baseline on 108 dead leaves image datasets varying in texture intensity, leaf size, and image size. Likelihood-only performance falls with increasing texture intensity and image size. Prior-only performance falls with decreasing leaf size and increasing maximal image dimension. All model-based observers strongly outperform the random baseline, and the ideal observer consistently outperforms the others by combining both information sources. The model provides a principled upper bound on segmentation performance for limited pixel sets, enabling comparisons with human observers and algorithms.

图像分割贝叶斯方法理想观察者死叶模型

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。