迭代覆盖森林框架：一种超级像素分割新方法

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"An Iterative Spanning Forest Framework for Superpixel Segmentation" 本文提出了一个迭代生成树框架（Iterative Spanning Forest, ISF）用于超像素分割，这是图像处理中的一个重要研究问题。ISF基于图像森林变换序列，允许用户选择四种关键参数：i) 种子采样策略，ii) 连通性函数，iii) 邻接关系，以及iv) 种子像素重计算过程，以在每一轮迭代中生成更优的连接超像素（在3D中为超体素）。ISF中的超像素结构上对应于以这些种子像素为根的生成树。文章介绍了五种不同的ISF方法，展示了其组件的不同选择。这五种方法与现有的最优基线方法在效果和效率方面进行了比较。实验涵盖了具有不同特性的2D和3D数据集，并应用到一个高级任务——天空图像分割。在补充材料中，证明了ISF的理论性质，结果显示，ISF的一些方法在效果和效率上可与最佳基线相媲美，甚至有所超越。超像素分割是将图像划分为均匀大小或属性相似的区域，以简化图像表示并提高后续处理的效率。ISF框架的独特之处在于其迭代性和可配置性，允许根据特定任务的需求调整参数。种子采样策略决定了分割的起点，连通性函数定义了像素间的相邻关系，邻接关系影响了超像素的形状和边界，而种子像素的重计算则有助于优化分割的质量。通过与其他最先进的方法进行比较，ISF展示了其在各种图像分割任务中的竞争力。实验部分不仅验证了ISF在不同数据集上的性能，还通过天空图像分割应用展示了其实用价值。这个应用通常需要精确地识别和分割天空区域，对于自动驾驶、无人机导航等领域的图像分析至关重要。 ISF提供了一个灵活且强大的工具，可以适应各种图像分割需求，尤其是在需要高精度和效率的场景下。通过调整其核心参数，研究人员和开发者能够为特定应用定制优化的超像素分割方案。

that the watershed transform from seeds is equivalent to a cut

in a minimum-spanning tree (MST). That is, the removal of

the arc with maximum weight from the single path in the MST

that connects each pair of seeds results a minimum-spanning

forest (i.e., a watershed cut). Such a graph cut tends to be better

than the normalized cut in boundary adherence, but worse in

superpixel regularity.

In the evolution of superpixel segmentation methods, it

is also worth mentioning Mean-Shift [40], Quick-Shift [41],

turbopixels [42], SLIC [1], geometric ﬂow [43], LSC [15],

and DBSCAN [21]. The Mean-Shift method produces irregular

and loose superpixels whereas the Quick-Shift algorithm does

not allow an user to choose the number of superpixels. The

turbopixel-based approaches can produce good superpixels,

but are computationally complex. C¸ iˇgla and Atalan [44] used

connected k-means algorithm with convexity constraints to

achieve superpixel segmentation via speeded-up turbopixels.

The method is still bit slow, and, as claimed by the authors,

fails to provide good boundary recall for complex images.

SLIC is by far the most commonly used superpixel method

[1]. It uses a regular grid for seed sampling. Once chosen, the

seeds are transferred to the lowest gradient position within a

small neighborhood. Finally, a modiﬁed k-means algorithm is

used to cluster the remaining pixels. This algorithm was shown

to perform better than many other methods (e.g., [42], [13],

[22], [23], [41]). However, the k-means algorithm searches for

pixels within a 2S × 2S window around each seed, where

S is the grid interval. For a non-regular seed distribution,

some pixels may not be reached by any seed. Indeed, this

might happen from the second iteration on and this labeling

inconsistency problem is only solved by post-processing. In

[43], Wang et al. proposed a geometric-ﬂow-based method

of superpixel generation. The method has high computational

complexity as it involves computation of the geodesic distance

and several iterations. LSC [15] and DBSCAN [21] are among

the most recent approaches. LSC models the segmentation

problem using Normalized Cuts, but it applies an efﬁcient

approximate solution using a weighted k-means algorithm to

generate superpixels. DBSCAN performs fast pixel grouping

based on color similarity with geometric restrictions, and then

merges small clusters to ensure connected superpixels.

A ﬁrst method based on the ISF framework appeared in [45]

and has been successfully used in a high level application [33].

It is considered in our experiments.

III. THE ISF FRAMEWORK

An ISF method results from the choice of each compo-

nent: inital seed selection, connectivity function, adjacency

relation, and seed recomputation strategy. The ISF algorithm

is a sequence of Image Foresting Transforms (IFTs) from

improved seed pixel sets (Section III-A). For initial seed

selection, we propose either grid or mixed entropy-based seed

sampling as effective strategies (Section III-B). The closest

minima of a gradient image to seeds obtained by grid sampling

is also evaluated in an attempt to solve the problem in

a single iteration. Examples of connectivity functions and

adjacency relations for 2D and 3D segmentations are presented

in Sections III-C and III-D, respectively. Two strategies for

seed recomputation are described in Section III-E. The ISF

algorithm is presented in Section III-G and its theoretical

properties are demonstrated in the supplementary material.

Section III-H discusses implementation issues and provides

the link to the code.

A. Image Foresting Transform

An image can be interpreted as a graph G = (I, A), whose

pixels in the image domain I ⊂ Z

are the nodes and pixel

pairs (s, t) that satisfy the adjacency relation A ⊂ I ×I are

the arcs (e.g., 4-neighbors when n = 2). We use t ∈ A(s) and

(s, t) ∈ A to indicate that t is adjacent to s.

For a given image graph G = (I, A), a path π

, t

, . . . , t

= ti is a sequence of adjacent pixels with ter-

minus t. A path is trivial when π

= hti. A path π

= π

·hs, ti

indicates the extension of a path π

by an arc (s, t). When we

want to explicitly indicate the origin of a path, the notation

s t

= ht

= s, t

, . . . , t

= ti is used, where s stands for

the origin and t for the destination node. A predecessor map is

a function P that assigns to each pixel t in I either some other

adjacent pixel in I, or a distinctive marker nil not in I — in

which case t is said to be a root of the map. A spanning forest

(image segmentation) is a predecessor map which contains no

cycles — i.e., one which takes every pixel to nil in a ﬁnite

number of iterations. For any pixel t ∈ I, a spanning forest

P deﬁnes a path π

recursively as hti if P (t) = nil, and

· hs, ti if P (t) = s 6= nil.

A connectivity (path-cost) function computes a value f(π

)

for any path π

, including trivial paths π

= hti. A path π

is optimum if f(π

) ≤ f (τ

) for any other path τ

in Π

(the set of paths in G). By assigning to each pixel t ∈ I one

optimum path with terminus t, we obtain an optimal mapping

C, which is uniquely deﬁned by C(t) = min

∀π

in Π

{f(π

)}.

The Image Foresting Transform (IFT) [11] takes an image

graph G = (I, A), and a connectivity function f ; and assigns

one optimum path π

to every pixel t ∈ I such that an

optimum-path forest P is obtained — i.e., a spanning forest

where all paths are optimum. However, f must satisfy certain

conditions, as described in [46], otherwise, the paths may not

be optimum.

In ISF, all seeds are forced to be the roots of the forest by

choice of f, in order to obtain a desired number of superpixels.

For any given seed set S, each superpixel will be represented

by its respective tree in the spanning forest P as computed by

the IFT algorithm.

B. Seed Sampling Strategies

Any natural image contains a lot of heterogeneity. Some

parts of the image can have really small variations in inten-

sity whereas some parts in the image can show signiﬁcant

variations. So, it is but natural to choose more seeds from

a more non-uniform region of an image. However, having a

grid structure for the seeds is also essential to conform to the

regularity of the superpixels. The proposed mixed sampling

strategy achieves both the goals. We use a two-level quad-

tree representation of an input 2D image. The heterogeneity

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