I Introduction
In the past few years, the massive collections of imagery on the Internet have inspired a wave of work on many interesting big data topics: scene reconstruction, location recognition, and online sharing of personal photo streams[2][3][4]. For example, one can easily download a huge number of photo streams associated with a particular place. By using features (e.g. SIFT), it is possible to automatically estimate correspondence information and reconstruct 3D geometry for the scene[5][6]. Imagine building a worldscale location recognition engine from all of the geotagged images from online photo collections, such as Flickr and street view databases from Google and Microsoft. However, it is a challenging task as the photo streams are neither aligned nor calibrated since they are taken in different temporal, spatial, and personal perspectives. Furthermore, with the occlusion of unexpected foreground objects, it is even more difficult to recover the whole scene or accurately identify overlapping regions between different photos.
To resolve the above issue, image inpainting is an effective solution. In this paper, we propose an automatic object removal algorithm for scene completion, which benefits subsequent large imagery processing. The core of our method is based on the structure and texture consistency. Our proposed approach has two major contributions. First, we develop a curve estimation approach to infer the potential structure of the occluded region on the image. Second, an orientated patch matching algorithm is designed for texture propagation. Our work has a broad range of applications including image localization[7][8], privacy protection[9][10][11], and other network based applications [12][13][14][15][16].
Ii Related Works
In the literature, image completion or inpainting has been intensively studied: in [17]
, Efros and Leung used a onepass greedy algorithm to render unknown pixels based on the assumption that the probability distribution of the pixel’s brightness is independent to the rest of the image when the spatial neighborhood is given. In
[18], the authors proposed an examplebased approach to fill in the missing regions. It worked well in filling in small gaps but not in large ones. The weakness of such approach is that it fails to preserve the potential structures. Jia et al. [19]designed an image inpainting method based on texturesegmentation and tensorvoting that created smooth linking structures in the occluded regions. This method sometimes introduces noticeable artifact due to the texture inconsistency. Criminisi
et al. [20] made an improvement by assigning inpainting orders based on the edge strength levels. Their algorithm used a confidence map and the image edges to determine the patch completion priority. However, the structures in the resulting images are not well preserved. The method in [21] produced a better result via structure propagation, while this approach requires more interaction. The completion results largely depend on the animator’s individual technique. Some other existing work also explored in[22][23][24].Iii Our Approach
The process of our framework is: for a given image, users specify the object for removal by drawing a closed contour around it. The enclosure is considered an unknown region that is inferred and replaced by the remaining region of the image. Figure 1 shows an example: the red car is selected as the removing object. In the resulting image Figure 1, the occluded region is automatically recovered based on the surrounding environment.
First let us define a set of notations for the rest of our paper. For an image , the target region for inpainting is denoted as ; the remaining part of the image is denoted as , which is also known as source region. The boundary contour along is denoted as . A pixel’s value is represented by , where x and y are the coordinates on the image. The surrounding neighborhood centered at is often called as a patch, denoted as . The coordinates of pixels inside the patch should be in the range: . These concepts are illustrated in Figure 1. In our framework, there are three phases involved to achieve the scene recovery:structure estimation, structure propagation, and remaining part filling.
Iiia Structure Estimation
In this phase, we estimate the potential structure in by finding all the possible edges. This procedure can be further decomposed into two steps: Contour Detection in and Curve Generation in .
IiiA1 Contour Detection in
We first segment the region by using gPb Contour Detector [25]. It is based on the idea of computing the oriented gradient signal on the four channels of its transformed image: brightness, color a, color b and texture channel. is the gradient signal, where indicates the center location of the circle mask that is drawn on the image and indicates the orientation. The gPb Detector is composed of two important components: mPb Edge Detector and sPb Spectral Detector [25]. We apply linear combination on mPb and sPb (factored by and ) according to the gradient ascent on Fmeasure:
(1) 
Thus a set of edges in can be retrieved via gPb. However, these edges are not in close form and have classification ambiguities. To solve this problem, we use the Oriented Watershed Transform[25] and Ultrametric Contour Map[1] (OWTUCM) algorithm to find the potential contours by segmenting the image into different regions. The output of OWTUCM is a set of different contours and their corresponding boundary strength levels as Figure 1 shows.
IiiA2 Curve Generation in
After obtaining the contours from the above procedure, salient boundaries in can be found by traversing . Our method for generating the curves in is based on the assumption: for the edges on the boundary in that intersects with the , it either ends inside or passes through the missing region and exits at another point of . Below is our algorithm for identifying the curve segments in :
In algorithm 1, it has three main parts: (a) collect all potential edges in that hits ; (b) identify optimal edge pairs from ; (c) construct a curve for each edge pair .
Edges Collection: The output of OWTUCM are contours sets and their corresponding boundary strength levels . Given different thresholds , one can remove those contours with weak . Motivated by this, we use the RegionSplit scheme to gradually demerge the whole into multiple subregions and extract those salient curves. This process is carried out on lines 19: at the beginning the whole region is considered as one contour; then iteratively decrease to let potential subcontours faint out according the boundary strength; Every time when any edges from the newly emerged contours were detected of intersecting with , they are put into the set .
Optimal Edge Pairs: the reason of identifying edge pairs is based on the assumption if an edge is broken up by , there must exist a pair of corresponding contour edges in that intersect with . To find the potential pairs from the edge list , we measure the corresponding enclosed regions similarities. The neighboring regions which is partitioned by the edge are used to compare with the corresponding regions of another edge . This procedure is described on lines of the algorithm 1. Each neighboring region is obtained by lowing down the threshold value to faint out more detailed contours as Figure 1 shows.
To compute the similarity between regions, we use the JensenShannon divergence [26] method that works on the color histograms:
(2) 
where and are the histograms of the two regions ; indicates the index of histogram bin. For any two edge , the similarity between them can be expressed as:
(3) 
and are the exclusive numbers in , where 1 and 2 represent the indices of the two neighboring regions in around a particular edge. The is the max value of the two comparing edges’ strength levels. The first multiplier is a penalty term for big difference between the strength levels of the two edges. To find the optimal pairs among the edge list, dynamic programming is used to minimize the global distance: , where and . To enhance the accuracy, a maximum constraint is used to limit the regions’ difference: . If the individual distance is bigger than the prespecified threshold , the corresponding region matching is not considered. In this way, it ensures if there are no similar edges existed, no matching pairs would be identified.
Generate Curves for each : we adopt the idea of fitting the clothoid segments with polyline stoke data first before generating a curve [27]. Initially, a series of discrete points along the two edges and are selected, denoted as . These points have a distance with each other by a prespecified value . For any three adjacent points , the corresponding curvature could be computed according to [28]:
(4) 
Combining the above curvature factors, a sequence of polyline are used to fit these points. The polylines are expected to have a possibly small number of line segments while preserving the minimal distance against the original data. Dynamic programming is used to find the most satisfied polyline sequence by giving a penalty for each additional line segment. A set of clothoid segments can be derived corresponding to each line segment. After a series rotations and translations over the clothoid, a final curve is obtained by connecting each adjacent pair with continuity [27]. Figure 1 demonstrates the curve generation result.
IiiB Structure Propagation:
After the potential curves are generated in , a set of texture patches, denoted as , need to be found from the remaining region and placed along the estimated curves by overlapping with each other with a certain proportion. Similar to [21], an energy minimization based method is proposed in a Belief Propagation (BP) framework. However, we have different definitions for the energy and message passing functions. The details are in the algorithm 2.
In the algorithm, the anchor points are evenly distributed along the curves with an equal distance from each other . These points represent the center where the patches () are synthesized, as shown in Figure 1. In practice, we define . The is the source texture patches in . They are chosen on from the neighborhood around . For the factor graph building, we consider each as a vertex and , where , are the two adjacent points.
In previous works [21][20], each have the same orientation as , which limits the varieties in the source texture. Noticing that different patch orientations could produce different results, we introduce a scheme called Adaptive Patch by defining a new formulas for and in the structure propagation.
Traditionally, the node energy is defined as the Sum of Square Difference(SSD) by comparing the known pixels in each patch with the candidate corresponding portion in . But this method limits the salient structure directions. Instead of using SSD on the two patches, a series of rotations are performed on the candidate patch before computing the similarity. Mathematically, can be formulated as:
(5) 
Where represents different rotations on the patch . Since the size of a patch is usually small, the rotation can be specified with an arbitrary number of angles. In our experiment, it is specified as . The parameter represents the number of known pixels in that overlap with the rotated patch . is a penalty term, the more number of overlapping pixels, the higher of similarity is assigned. So we use to discourage the patches with smaller number of sharing pixels. Here, the percentage is expressed as ( is the length of ). is the corresponding normalized scalar. Thus the best matching patch is represented by two factors: index and rotation .
In a similar way, the energy on each edge can be expressed as:
(6) 
Here and are the indices of the two adjacent patches in . A penalty scheme is applied to the similarity comparison. The two parameters for indicate the index and rotation for the source patches in . The messages propagation is derived from the results of the above energy functions. We adopt a similar method as [21], where the message passes by patches is defined as:
(7) 
Through iterative updating on the BP graph, an optimal decision of for the patches in is made by minimizing the nodes’ energy. This principle can be formulated in the definition below:
(8) 
Where is one of the neighbors of the patch : . is the optimal index for the matching patch. To achieve minimum global energy cost, dynamic programming is used. Each assignment for or is considered as a stage. In each stage, the choices of represent different states. The edge represents the transit cost from state at stage to state at stage . Starting from , an optimal solution is achieved by minimizing the total energy from last step:
(9) 
where represents a set of different total energy values at current stage . In the situation of multiple intersections among curves , we adopted the idea in [21], where readers can refer for further details.
IiiC Remaining Part Filling:
After the curves are generated in , we fill the remaining regions by using the exemplarbased approach in [20]. The is getting smaller and smaller by spreading out the known pixels in a certain order. To enhance the accuracy, all the pixels in the above generate patches along the estimated curves are assigned with a precomputed confidence value based on the confidence updating rule in [20].
Iv Experiments
In our experiments, we first evaluate our proposed approach in terms of structure coherence by comparing our result with the one in [20] that works on the wellknown Kanizsa triangle. As shown in Figure 2, the white triangle in the front is considered as the occluded region that needs to be removed. First, a structure propagation is carried out based on the detected edges along . The dash lines in Figure 2 indicate the estimated potential structures in . Texture propagation is applied to the rest of the image based on the confidence and isophote terms. One can notice both the triangle and the circles are well completed in our result Figure 2 comparing with Criminisi’s method in Figure 2.
To further demonstrate the performance, a set of images are used for scene recovery: ranging from indoor environment to natural scenes. Figure 3 shows an indoor case where highly structured patterns often present, such as the furniture, windows, walls. The green bottle on the office partition is successfully removed while preserving the remaining structure. In this example, three pairs of edges are identified and connected by the corresponding curves that are generated in the occluded region . Figure 3 and 3 show the results of removing trees in the nature scenes. Several curves are inferred by matching the broken edges along and maximizing the continuity. We can notice the three layers of the scene (sky, background trees, and grass land) are well completed. In Figure 3, it shows a case that a perching bird is removed from the tree. Our structure estimation successfully completes the tree branch with smooth geometric and texture transitions.
V Conclusion
In this paper, we present a novel approach for foreground objects removal while ensuring structure coherence and texture consistency. The core of our approach is using structure as a guidance to complete the remaining scene. This work would benefit a wide range of applications especially for the online massive collections of imagery, such as photo localization and scene reconstructions. Moreover, this work is applied to privacy protection by removing people from the scene.
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