I Introduction
Image segmentation is an essential tool to analyze the image content. The aim is to split the image into similar regions with respect to some priors (e.g.
, object, color or texture). To decrease the computational time and to improve the accuracy of unsupervised segmentation, superpixel decomposition methods have been proposed. These methods group the pixels into homogeneous regions while trying to respect image contours. Superpixels drastically decrease the image content dimension while preserving geometrical information, contrary to multiresolution approaches. For instance, small objects that disappear at small resolution levels, can still be contained into single superpixels. Hence, superpixels have naturally become key building blocks of many computer vision works such as: contour detection
[1], face labeling [2], object localization [3], or multiclass object segmentation [4, 5].Superpixel methods can be divided in two categories that provide either irregular or regular decompositions. With irregular methods, superpixels can be stretched, with very different sizes, and may overlap with several objects contained in the image. Moreover, very small superpixels can be extracted, and without enough pixels, significant descriptors are difficult to estimate. On the contrary, regular methods provide superpixels with approximately the same size, and enable to compute more robust descriptors.
There is no general rule for the definition of an optimal superpixel method since the desired properties depend on the tackled application. A compromise must be made between: computational time, adherence to image boundaries, and size and shape regularity of the superpixel decomposition.
On the one hand, accurate contour adherence is for instance reached with irregular methods (e.g., [6]) that allow very stretched superpixel decompositions based on color similarity. On the other hand, it appears crucial for superpixelbased object recognition methods to use regular decompositions [4, 5]. Moreover, when facing video tracking of superpixels [7], fast and regular approaches are suitable to consider the time consistency of the decomposition. Regularity is thus crucial to accurately analyze object trajectories in a scene. In Figure 1, we show an example of a reconstructed image from the irregular method SEEDS [6] and from our regular method SCALP. The image is computed by the average color on each superpixel. SCALP provides a much more visually satisfying result due to regularity and accuracy of superpixel boundaries.
Initial image  SEEDS [6]  SCALP 
Irregular Superpixel Methods. Classical methods, such as the watershed approach [9], compute decompositions of highly irregular size and shape. In this context, starting from an initial clustering, Mean shift [10] or Quick shift [11] approaches use histogrambased segmentation but require high computational time. By considering pixels as nodes of a graph, faster agglomerative clustering can be obtained [12]. In addition to the lack of control over the superpixels shape, all these methods present another main drawback. They do not allow to directly control the number of superpixels, which is a major issue when using superpixels as lowlevel representation to reduce the computational time for a dedicated task.
More recently, the SEEDS method [6] has been proposed to produce a decomposition in a reduced computational time. This approach is initialized with a regular grid and updates superpixel boundaries with block and pixel transfers. Despite its initial regular grid, this method provides superpixels with irregular shapes. Finally, the authors report significantly degraded results when trying to regularize the superpixel shape with compactness constraint [6].
Regular Superpixel Methods. When considering more general applications than contour adherence, stateoftheart superpixelbased methods consider regular decompositions (e.g., [7, 5]). Classical methods are based on region growing, such as Turbopixels [13] using geometric flows, or graphbased energy models [14, 15]. In [16], the watershed method is adapted to produce regular decompositions using a spatially regularized gradient.
Recently, the Simple Linear Iterative Clustering (SLIC) superpixel method was proposed in [17], and its extensions, e.g., [18, 19]. This method performs an accurate color clustering, providing regular superpixels, while being order of magnitude faster than graph approaches [14] or [15], and achieves stateoftheart results on superpixel metrics. However, since a compactness parameter is set to enforce the superpixel shape regularity, SLIC can fail to adhere to image contours, as for other regular methods [13, 14].
Several works have attempted to enhance the performance of regular methods in terms of contour adherence by using a contour prior information. Although methods to compute regions from contours have been proposed (e.g., [20]), they do not allow to control the size, shape and number of regions, and therefore cannot be considered as superpixel decomposition methods. In [21], contour priors are used to compute a presegmentation using the normalized cuts algorithm [22]. This segmentation is considered as a hard constraint to provide a finer regular decomposition. However, the decompositions based on normalized cuts are highly tuned and computationally expensive, while they are far from stateoftheart results in terms of contour adherence. In [23], the decomposition is constrained to fit to a grid, named superpixel lattice. This decomposition uses a contour map as input to determine this lattice, and iteratively refines it using optimal cuts. The method finally produces superpixels of regular sizes but irregular shapes, that are visually unsatisfactory [23]. Moreover, the method appears very dependent on the contour prior. In more recent works, such as [19], superpixels are locally forced to adhere to contours by considering a precomputed gradient used as constraint to compute the boundaries of superpixels.
Contributions. In this paper, we propose a fast method to directly include a contour prior in a superpixel clustering framework, and not as hard prior from a presegmentation step. To that end, the distance computed when trying to associate a pixel to a superpixel is enhanced by considering image feature and contour intensity on a linear path to the superpixel barycenter. The decomposition provides superpixels of regular sizes and shapes that respect color homogeneity, and their boundaries are computed according to the contour prior.
We provide a detailed evaluation of our method on the standard Berkeley Segmentation Dataset [8], compared to stateoftheart methods on superpixel and contour detection metrics. We demonstrate the regularity of our decomposition, that obtains the best results on most of the compared metrics.
Ii SCALP Framework
The SCALP framework generalizes the iterative clustering algorithm of [17]. Thanks to the introduction of the linear path within the clustering, a more regular decomposition can be obtained. Moreover, prior information such as contour maps can be naturally included within the path to softly constrain the decomposition, as illustrated in Figure 2.
ICI PAS CLAIR (sur le fait que tu calcules sur un reduced set: c’est trop de detail a ce moment du papier) During the clustering, we compute on a reduced set of pixels, the contour intensity on the path to the cluster center, to make sure that no boundary is crossed when associating a new pixel to a superpixel. JE METTRAIS PLUTOT:
In this section, we first present the iterative clustering framework. Then, we define the linear path to the superpixel barycenter. Next, we propose to use this path to include relevant information for superpixel clustering, by proposing a new color distance term. We finally propose a fast method to integrate a contour prior into our framework.
Iia Simple Linear Iterative Clustering
As previously stated, SLIC [17] is one of the most efficient and simplest superpixel frameworks. In its default settings, it only takes the number of superpixels as parameter. The decomposition is initialized with a regular grid, with blocks of size , and an iterative clustering, spatially constrained into a window of fixed size , is performed for all superpixels. The size is defined by the ratio between the number of pixels and the number of superpixels, such that . With this constraint, roughly equally sized superpixels are provided, ensuring the decomposition regularity.
Each superpixel of SLIC is described by a cluster containing the average feature information and spatial barycenter of all pixels . In [17], the clustering is performed in the CIELab color space. Therefore, each superpixel at a given iteration is described by its cluster =, containing the average CIELab color feature on pixels and =, the barycenter of . At each iteration, and for each cluster , all pixels =, within a square window of size centered on the barycenter , are tested to be associated to by computing a spatial distance and a color distance The pixel is assigned to the cluster that minimizes the sum of these two distances. Despite its basic framework, SLIC achieves results that are comparable to stateoftheart methods and even outperforms irregular approaches such as [6], in the contour detection evaluation framework of [24].
The distance between the pixel and the cluster is computed as:
(1)  
(2)  
(3) 
with the parameter setting the decomposition compactness, i.e., the compromise between the color distance and spatial distance . The higher is, the more regularized (squared) is the shape of the superpixels. With a small , the superpixel decomposition follows more tightly the image color boundaries but their size and shape are more variable.
The framework in [17] provides regular superpixels that can adhere to image contours. However, this adherence can still be enhanced by considering accurate contour information as prior. By introducing the notion of linear path, SCALP computes a generalized color distance term that improves the homogeneity of the color clustering and the regularity of the superpixels shape. We also propose to integrate the contour prior information as a soft constraint in this new color distance to enforce the adherence to image contours.
IiB Linear Path to the Cluster Center
To enforce the color homogeneity within a superpixel and contour adherence, we consider the color and contour intensities on the linear path between pixels and their corresponding superpixel barycenter.
We thus define the path of pixels between a pixel and a superpixel barycenter . By considering information along this path, SCALP is able to enhance the relevance of the color distance. Note that the more pixels are considered in , the higher the computational cost is. Hence, we propose to use [25] to only get the positions of pixels on the direct path between the pixel and the barycenter of superpixel , as illustrated in Figure 3. The considered pixels (in red) are those that intersect with the segment (red arrow) between , the position of pixel (in black), and , the barycenter of superpixel (in blue). By considering this simple linear path instead of a more sophisticated geodesic one [26], we limit the computational cost and enforce the decomposition compactness.
IiC Improved Color Distance to Cluster
As in [17], the spatial distance between a processed pixel and a cluster is only computed between positions of and its barycenter . However, the CIELab color distance may now be computed on , the set of pixels on the path to the superpixel barycenter. The new color distance is thus defined as:
(4) 
where weights the influence of the color distance along the path between and . Since color on the linear path to the barycenter should be close to the average color of the superpixel, SCALP naturally enforces the decomposition compactness and favors uniform color distribution.
IiD Adherence to Contour Prior
When associating a pixel to a superpixel cluster, we want to favor the color homogeneity, the proximity to the cluster barycenter and the adherence to image contours. We assume that a soft contour prior map is available. Such map typically sets if a contour is detected, otherwise , at pixel . A fast and efficient way to integrate this prior information is to weight the color distance (4) by , the sum of contour intensity on defined as:
(5) 
where and are parameters that weight the influence of the contour prior along the linear path. When a contour intersects the path between a pixel and a cluster barycenter, such term tends to prevent this pixel to be associated to the cluster . The proposed distance to minimize during the clustering is finally defined as:
(6) 
where is the compactness parameter, i.e., setting the tradeoff between color distance and spatial distance . The higher is, the more regular, i.e., compact, is the superpixel shape. On the other hand, small values of allow a better adherence to image color boundaries, producing superpixels of more variable sizes and shapes. By setting in (4) and in (5), the proposed distance (6) reduces to the standard distance used in [17]. The SCALP algorithm is summarized in Algorithm 1.
Remark: Note that although the algorithm starts from an initial regular grid, the spatial barycenter of a superpixel may, in very rare cases, fall outside the superpixel after a few iterations. Having a cluster center outside the superpixel impacts the computation of the linear path. Hence, if the barycenter is not contained into the superpixel , we consider the projected position to compute the linear path to the center , which is computed as:
(7) 
IiE Contour Prior
SCALP can directly consider a contour prior into the clustering framework. Therefore, our decomposition is not constrained by a presegmentation step. This contour prior can either be soft or hard, i.e., having values between 0 and 1 or being binary, and can be computed by any contour detection method (see for instance [1] and references therein). In Section IIIB, we report results obtained using different contour detection methods [27], [28], [29].
Iii Results
Iiia Validation Framework
IiiA1 Dataset
We evaluate our method on the standard Berkeley Segmentation Dataset (BSD) [8]. The BSD contains 500 images of
pixels divided into three sets: 200 for training, 100 for validation and 200 for testing. For each image, at least 5 ground truth decompositions from manual segmentations are also provided to compute evaluation metrics. We report results of SCALP and other compared methods on the 200 images of the test set.
IiiA2 Metrics
To evaluate the performances of our framework and compare to the stateoftheart methods, we use the standard superpixel evaluation metrics: boundary recall (BR), undersegmentation error (UE) and achievable segmentation accuracy (ASA). To compare the regularity of superpixel shape of different decompositions, we report the compactness measure introduced in [30]. In the following, for an image , a human ground truth segmentation is denoted , where is a segmented region of the scene, is the number of regions within the decomposition, and denotes the cardinality. Reported values are averaged results on all ground truths. To quantify the results of contour detection performance, we report the precision (P) recall (R) curves [24].
Boundary Recall. This measure evaluates the percentage of ground truth contours that overlap, within an pixel distance, with the boundaries of the computed superpixel decomposition . The BR metric is defined as follows:
(8) 
with = when is true and otherwise, and = as in [6].
Achievable Segmentation Accuracy. The ASA is an upper bound measure that computes the maximum object segmentation accuracy by taking superpixels as units. For each superpixel , the largest possible overlap with a ground truth segment is computed and averaged as follows:
(9) 
Undersegmentation Error. This measure evaluates the percentage of pixels that cross ground truth boundaries. With an accurate superpixel decomposition with respect to a given ground truth, superpixels should overlap with only one object. The undersegmentation error (UE) is computed as:
(10) 
Compactness measure. The compactness (CO) measure for a superpixel decomposition is defined as in [30]:
(11) 
where defines the perimeter of the superpixel . High values indicates more compact superpixels.
PrecisionRecall. The PR framework [24] evaluates the contour detection accuracy. It can be used to measure the contour detection performances of segmentation or superpixel algorithms. The PR curves are computed from a set of input maps, which values represent the confidence in being on an image boundary. When evaluating superpixel methods, these maps can be computed by averaging superpixel boundaries obtained from decompositions at multiple scales. As in [6], we considered 12 scales, ranging from 6 to 600 superpixels, to compute the boundary maps. We rank the methods according to their maximum measure defined as , where (precision) is the percentage of accurate detection among the computed contours, and (recall) is the percentage of detected ground truth contours.
IiiA3 Parameter Settings
SCALP was implemented with MATLAB using CMEX code, on a standard Linux computer. The number of clustering iterations is set to . We set to in the proposed color distance (4), to in (5), and to , to adjust to the superpixel size. The compactness parameter is set to in (6) as in [17]. These parameters offer a good tradeoff between adherence to contour prior and compactness. In the following, if not mentioned, we use a prior from the contour detection method of [29].
IiiB Influence of Parameters
We first measure the influence of parameters within the proposed framework. In Figure 4(a), we provide PR curves for different distance settings. Contributions of the new the color distance (4) and the additional contour intensity (5) computed on the linear path to the superpixel barycenter both increase the accuracy of the decomposition with respect to ground truth segmentations. The complete SCALP algorithm, i.e., using color distance and contour intensity, provides the best results and outperforms the standard method proposed in [17].
(a)  (b) 
We also investigate the influence of the contour prior. In Figure 4(b), we provide PR curves obtained by using the
globalized probability of boundary
algorithm [27], a method using learned sparse codes of patch gradients [28], and a structured forests approach [29] for contour detection. Results are also improved with respect to the contour detection accuracy. In the following, results are computed using [29].IiiC Comparison with StateoftheArt Methods
We compare the proposed approach to the following stateoftheart methods: Quick shift (QS) [11], Turbopixels (TP) [13], a graph cut approach (GC) [14], SLIC [17] and SEEDS [6]. Note that TP and GC enforce regularity and thus provide very consistent decompositions at the expense of lower contour adherence. All provided results are computed with the same validation framework, described in Section IIIA, with codes provided by the authors and used with their default settings.
In Figure 5, we provide PR curves with their maximum measure, and report the standard BR (8), ASA (9) and UE (10) metrics. SCALP is ranked on PR, providing the higher measure (0.676). On superpixel metrics, it is ranked on ASA and UE, and on BR.
Although high BR results indicate that ground truth boundaries are well detected by the superpixels, this measure does not consider the false detection. Therefore, irregular methods such as [6], that produces very stretched superpixels with much more boundary pixels can obtain higher BR results. Better PR performances indicate that SCALP very accurately detects object contours with a lower false detection rate. The UE metric is penalized when superpixels overlap with multiple objects. Hence, SCALP superpixels overlap with a lower number of ground truth segments. The ASA evaluates the consistency of a decomposition with respect to the objects within an image, thus enhancing the largest possible overlap. Higher ASA results for SCALP also indicate that the produced superpixels are better contained in the image objects.
The regularity of the proposed SCALP framework is confirmed with Table I, which reports the compactness measure (11) for the best compared methods. The provided results are averages obtained on all image decompositions, on the same scales as the ones used to compute the PR curves. SCALP obtains the most regular superpixels, even improving the results of SLIC [17].
Finally, Figure 6 illustrates the decomposition results obtained with SCALP and the compared approaches on example images. SCALP appears to provide more regular superpixels while tightly following the image contours.
SCALP achieves the best stateoftheart segmentation and contour detection performance, while providing a regular superpixel decomposition, in a limited computational time, i.e., less than s per image of the BSD.
Iv Conclusion
In this work, we propose a generalization of the superpixel clustering framework of [17], by considering image feature and contour intensity on the linear path from the pixel to the superpixel barycenter. The contour prior information enhances the adherence to the object boundaries.
The proposed SCALP method provides superpixels of more regular shape, according to the compactness measure. SCALP also obtains stateoftheart results, outperforming [17] on superpixel metrics, and obtains the higher measure among the compared methods. Finally, our fast integration of the contour prior within the framework enables to obtain the decomposition in a limited computational time.
Future works will focus on SCALP adaptation to supervoxel decomposition, for video and 3D image processing.
Acknowledgment
This study has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the Investments for the future Program IdEx Bordeaux (ANR10IDEX0302), Cluster of excellence CPU and TRAIL (HRDTI ANR10LABX57).
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