Superpixel-based Color Transfer

TL;DR

This paper introduces a rapid superpixel-based color transfer method that efficiently matches and transfers colors between images, improving speed and visual quality over existing techniques.

Contribution

The paper presents a novel superpixel-based approach with an approximate nearest neighbor matching algorithm and a fusion framework for improved color transfer.

Findings

Faster color transfer compared to traditional methods

Enhanced visual quality in transferred images

Competitive results against state-of-the-art techniques

Abstract

In this work, we propose a fast superpixel-based color transfer method (SCT) between two images. Superpixels enable to decrease the image dimension and to extract a reduced set of color candidates. We propose to use a fast approximate nearest neighbor matching algorithm in which we enforce the match diversity by limiting the selection of the same superpixels. A fusion framework is designed to transfer the matched colors, and we demonstrate the improvement obtained over exact matching results. Finally, we show that SCT is visually competitive compared to state-of-the-art methods.

Tables

Table 1. Table 1 : Computational times of the compared methods

Method	$480\times 640$	$480\times 640$	$480\times 640$
Histogram matching [25]		0.482	0.574
[25]		0.482	0.574
SCT		0.482	0.574

Equations

$$C(A_i,A_j)=($$

$$+(D(A_j,B_{(i)})-D(A_j,B_{(j)})).$$

$$A_t(p)=\frac{{\sum }_j\omega (p,A_j){\bar{C}}_{B_{(j)}}}{{\sum }_j\omega (p,A_j)},$$

$$\omega (p,A_j)=\exp \left(-\left((p-\overline{A_j}{)}^T{Q}_i^{-1}(p-\overline{A_j})-\sigma (p)\right)\right),$$

$$Q_i=Q(A_i)=\left(\begin{array}{cc}{\delta }_s^{2}Cov(X_i)& 0\\ 0& {\delta }_c^{2}Cov(C_i)\end{array}\right).$$

$$M_s(S_i)=Cov(X_i)=\left(\begin{array}{cc}Cov(y_i,y_i)& Cov(y_i,x_i)\\ Cov(x_i,y_i)& Cov(x_i,x_i)\end{array}\right),$$

$$M_c(S_i)=Cov(C_i)=\left(\begin{array}{ccc}Cov(r_i,r_i)& Cov(r_i,g_i)& Cov(r_i,b_i)\\ Cov(g_i,r_i)& Cov(g_i,g_i)& Cov(g_i,b_i)\\ Cov(b_i,r_i)& Cov(b_i,g_i)& Cov(b_i,b_i)\end{array}\right).$$

Full text

**Index Terms— ** Color transfer, Superpixels

1 Introduction

Color transfer consists in modifying the color distribution of a target image using one or several reference source images. The produced result must be consistent with the target image structure, and computational time is an important issue to process large images or video sequences.

Color transfer. Initiated by [1], many approaches have been proposed to transfer color statistics in different color spaces [2, 3, 4, 5]. Optimal transportation tools have also been intensively studied to match and transfer the whole color distribution  [6, 7, 8]. Nevertheless, as underlined in [9], since color distributions between images may be very different, the exact transfer of the color palette may produce visual outliers. Relaxed optimal transport models, that do no exactly match color distributions, have then been proposed to tackle this issue [10], but they rely on time consuming algorithms. Moreover, when the process is only performed in the color space, incoherent colors may be transfered to neighboring pixels. Artifacts such as JPEG compression blocks, enhanced noise or saturation then become visible [11], unless considering object semantic information [8]. In [12], an EM approach is used to estimate a Gaussian mixture model in color and pixel space, since the pixel location helps to preserve the image geometry. However, a major limitation is the matching of clusters using a greedy approach based on nearest-neighbor criterion, with no control on the selected source colors. In [13], a relaxed optimal transport model is applied to color transfer using superpixel lower-level representation.

Superpixels. These decomposition methods reduce the image dimension by grouping pixels into homogeneous areas [14, 15, 16]. They have become widely used to reduce the computational burden of various image processing tasks such as multi-class object segmentation [17], object localization [18] or contour detection [19]. Generally, the irregular geometry of the decompositions makes difficult their use into standard processes. However, for color transfer application, superpixels become particularly interesting since they enable to describe consistent color areas, and matches can be found regardless of the superpixel neighboring structure.

Superpixel-based approaches such as [13, 20] allow a better adaptation to color histograms and image content, but still require important computational cost. Except for tracking applications [21], fast superpixel matching methods have been little investigated. For instance, in [22], the PatchMatch (PM) algorithm [23] that finds approximate nearest neighbor (ANN) patches between images is adapted to graphs, and [24, 25] consider it in the superpixel context.

Contributions. In this work, we propose a fast superpixel-based color transfer method (SCT). An example result of SCT is given in Figure 2. To select the color candidates, we use the fast and robust PM algorithm, that we adapt to handle superpixels [25]. Contrary to [12], we propose a method to constrain the ANN search process to limit the selection of the same superpixels in the source image. Throughout the paper, we demonstrate the significant improvement obtained with this constraint, that enables to enforce the match diversity and to capture a larger color palette, similarly to [13]. The selected colors are then transfered by a color fusion approach inspired from the non-local means framework [26]. Finally, we show that SCT produces accurate color transfer in low computational time thanks to the superpixel representation.

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The aim of color transfer is to correct or strongly modify the color distribution of a target image using one or several reference source images. The produced result must be visually satisfying and consistent with the target image structure, and computational time is an important issue to process large images or video sequences. Many methods have been proposed to perform color transfer. For instance,

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In the context of color transfer, superpixels have been used is several works . Superpixel methods reduce the image dimension by grouping pixels into homogeneous areas [14, 15, yao2015, 16]. In the past years, they have become widely used to reduce the computational burden of various image processing tasks such as multi-class object segmentation [17], object localization [18] or contour detection [19]. Generally, the irregular geometry of the superpixel decompositions makes difficult their use into standard processes. However, for color transfer application, superpixels become particularly interesting since they enable to describe consistent color areas, and matches between images can be found regardless of the superpixel neighboring structure. In … Finally, in , the matching between superpixels is defined by an optimal transport problem.

Besides tracking applications [21], superpixel matching methods have been little investigated in the literature. For instance, in [22], the PatchMatch (PM) algorithm that finds approximate nearest neighbor (ANN) patches between images is modified to handle graphs, and [24] adapts this work to superpixel matching using learned distance metric.

Contributions. In this work, we propose a fast superpixel-based color transfer method (SCT). To select the color candidates, we use the robustness and convergence speed of the PM algorithm, that we directly adapt to handle superpixels, hence designing a fast superpixel ANN matching algorithm. We propose a method to constrain the ANN search process to limit the selection of the same superpixels in the source image. Throughout the paper, we demonstrate the substantial improvement obtained with this constraint, that enables to enforce the match diversity and to capture the a larger palette of the source image. The selected colors are then transfered by a color fusion approach inspired from the non-local means framework [26].

Finally, we show that our method produces accurate color transfer with low computational time thanks to the superpixel representation. Moreover, the color transfers obtained by SCT that are more visually satisfying or equivalent to the ones of state-of-the-art methods.

2 Superpixel-based Color Transfer Method

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In this section, we describe the superpixel ANN search [25], based on PM. We then present the proposed algorithm to constrain the ANN search to enforce the matches diversity and the novel superpixel-based color fusion framework.

2.1 ANN Superpixel Matching

PatchMatch algorithm. The PatchMatch (PM) method [23] computes correspondences between pixel patches of two images $A$ and $B$. It exploits the assumption that if patches are matched between $A$ and $B$, then their respective adjacent neighbors should also match well. Such propagation, associated with a random selection of patch candidates, enables the algorithm to have a fast convergence towards good ANN.

PM is based on three steps. The first one randomly assigns to each patch of $A$, a corresponding patch in $B$. An iterative refinement process is then performed following a scan order (top left to bottom right) to refine the correspondences with the propagation and random search steps. For a patch $A_{i}\in A$, the aim is to find the match $B_{(i)}\in B$ that minimizes a distance $D(A_{i},B_{(i)})$, for instance the sum of squares differences of color intensities. During propagation, for each patch in $A$, the two recently processed adjacent patches are considered. Their matches in $B$ are shifted to respect the relative positions in $A$, and the new candidates are tested for improvement. Finally, the random search selects candidates around the current ANN in $B$ to escape from local minima.

Adaptation to superpixel matching. Several issues appear when considering the PM algorithm to the matching of superpixels [25]. Since superpixels decompose the image into irregular areas, there is no fixed adjacency relation between the elements. First, a scan order must be defined to process the superpixels. Then, during propagation, the decomposition geometry being also different in the image $B$, the shift of the neighbor cannot be directly performed. A solution is to select the candidate with the most similar relative orientation computed with the superpixel barycenters. Figure 3 illustrates the selection of a candidate during propagation. Such adaptation of PM provides a fast superpixel ANN matching algorithm that produces an accurate selection of colors to transfer.

2.2 Constraint on Match Diversity

In practice, the ANN search may converge towards exact matching, almost providing the nearest neighbors. The aim of color transfer is to globally capture the source color palette. If the source image contains one or several elements that match well the color set of the target image $A$, the ANN search may lead to the same match in $B$. The color transfer would thus provide a result very close to $A$. Figure 6 illustrates this issue. Since the source image also contains red colors, all superpixels of the target image find a close red match in the source space, leading to no color transfer.

To enforce the match diversity and capture a larger color palette of the source image, we propose to constrain the ANN search and to restrict the number of associations to the same element. To do so, we set a parameter $\epsilon$ that defines the maximum number of selection of the same superpixel. Such constraint requires the number of source elements $|B|$ to be such that $|A|\leq\epsilon|B|$. In Figure 6, with $\epsilon=1$, the target superpixels now capture the global palette of the source image. First, we make sure that the initialization step respects this constraint when randomly assigning the correspondences. Then, during the following iterative process, a superpixel $A_{i}$ can be assigned to a superpixel $B_{k}$, only if less than $\epsilon$ superpixels in $A$ are already assigned to $B_{k}$. If $B_{k}$ is already matched by $\epsilon$ elements in $A$, one superpixel $A_{j}$ assigned to $B_{k}$ must be sent to another superpixel in $B$ to allow $A_{i}$ to match $B_{k}$. We propose to compute the cost of sending a superpixel $A_{j}$, currently matched with $B_{k}$, towards $B_{(i)}$, the current correspondence of $A_{i}$, thus making a switch between the matches, and ensuring the respect of the constraint set by $\epsilon$. For all superpixels $A_{j}$ matched to $B_{(j)}=B_{k}$, the switching cost is considered as follows:

[TABLE]

If a superpixel $A_{j}$ reduces the global matching distance, i.e., if the cost $C<0$, we proceed to the following assignments: $\underset{A_{j}}{\text{argmin}}(C(A_{i},A_{j}))\rightarrow B_{(i)}$ and $A_{i}\rightarrow B_{(j)}=B_{k}$.

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Comparison to optimal assignment. The proposed ANN algorithm with $\epsilon=1$ approximates the optimal assignment problem, addressed with the Hungarian or Munkres algorithms [27]. Given two sets of elements $\{A_{i}\}_{i\in\{1,\dots,|A|\}}$ and $\{B_{j}\}_{j\in\{1,\dots,|B|\}}$ with $|A|\leq|B|$, the aim is to find to each $A_{i}$, an assignment $B_{(i)}$ that can only be selected once, and to minimize the global distance between the matched elements.

In Figure 7, we consider two close images of $1920{\times}800$ pixels [28]. We show the target image reconstruction $\widetilde{A}$ from the matched superpixels average colors and compare total matching distance and computational time between our approach, optimal resolution [27], and to random superpixel assignments, i.e., the initialization step of our algorithm. Our fast superpixel ANN method provides close results to the optimal resolution while being order of magnitude faster.

2.3 Color Fusion Framework

Our matching framework provides an ANN in $B$ to each superpixel of $A$. The aim is then to transfer the color of the matches to compute the color transfer image $A_{t}$ while preserving the structure of the target $A$. Since the matched superpixels are very likely to have different shapes, there are no direct pixel associations between elements, and source colors cannot be directly transfered to $A$ at the pixel scale. The average colors of superpixels in $B$ can be transfered to the ones in $A$ but it would give a piece-wise color transfer result.

We propose to consider the average colors from the matched superpixels in a non-local means fusion framework [26]. Hence, all matched colors can contribute to the color computation of each pixel in $A_{t}$. Such approach enables to increase the number of color candidates and leads to new potential ones that adapt well to the target image content. A superpixel $A_{i}$ is described by the set of positions $X_{i}$ and colors $C_{i}$ of the contained pixels $p$, such that $A_{i}=[X_{i},C_{i}]=[(x_{i}/N_{x},y_{i}/N_{y}),(r_{i},g_{i},b_{i})/255]$, with $N_{x}{\times}N_{y}$ the size of image $A$. To compute the new color $A_{t}(p)$ of a pixel $p$, the weighted fusion of the matched colors is performed based on color and spatial similarity:

[TABLE]

with $\bar{C}_{B_{(j)}}$, the average color of the match of $A_{j}$ in $B$, and $\omega(p,A_{j})$ the weight that depends on the distance between the considered pixel $p\in A_{i}$ and the superpixel $A_{j}\in A$. This weight is computed similarly to a Mahalanobis distance:

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where $\sigma(p)$ sets the exponential dynamic and is set such that $\sigma(p)=\underset{j}{\min}{\left((p-\bar{A_{j}})^{T}Q_{i}^{-1}(p-\bar{A_{j}})\right)}$, and $Q_{i}$ includes spatial and colorimetric covariances of the pixels in $A_{i}$:

[TABLE]

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with,

[TABLE]

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The SCT steps are illustrated in Figure 8. We show the decomposition of images into superpixels with average colors, the matched source colors, and results of color fusion and post-processing with a color regrain [29].

3 Color Transfer Results

3.1 Parameter Settings

SCT is implemented with MATLAB using C-MEX code. Superpixel decompositions are computed using [16] such that each superpixel approximately contains $500$ pixels. The superpixel matching is performed on normalized cumulative color histogram features and the number of ANN search iterations is set to $20$. The covariance parameters in Eq. (4) are set such that $\delta_{s}$=$100\delta_{c}$ and $\delta_{c}$=$0.1$ in order to favor spatial consistency. Finally, unless mentioned, $\epsilon$ is set to $3$ and the results are slightly refined using a color regrain [29].

Our method produces results in very low computational time due to the use of superpixels, i.e., less than $1$s for images of $480{\times}360$ pixels. Decompositions are computed with [16] in less than $0.4$s, matching is performed in approximately $0.1$s and color fusion takes $0.25$s to provide the color transfer.

3.2 Influence of Match Diversity

Additionally to Figure 6, we illustrate in Figure 9 the influence of the $\epsilon$ parameter that limits the source superpixel selection. It appears that even fast ANN search may lead to the same best match, as shown with the maps corresponding to the selection of source superpixels. For instance, most target superpixels of the white flower match the only white superpixel in the source image, leading to almost no color transfer. With the proposed method, we select accurate matches while capturing the global color palette of the source image.

3.3 Comparison with State-of-the-Art Methods

In this section, we compare the results of SCT to various methods based on optimal transport [6], histogram transfer with a variational model [4] and 3D color gamut mapping [5]. Figure 10 illustrates color transfer examples for all methods.

SCT produces more visually satisfying results than the ones of the compared methods. The colors are relevantly transfered to the target image with respect to the initial grain and exposure. For instance, on the first image (top row), [6], [4] and [5] produce color transfers that strongly modify the illumination of the target image. All compared methods except SCT fail at transferring the blue color from the desert sky into the sea (middle row), and the orange color of the stones to the grass of the moutain (bottom row). Contrary to the compared methods, we consider a selection of the source colors and our fusion model enables to adapt to the target image, preserving its structure and initial exposure. Finally, while SCT results are computed in less than $1$s, while other models such as [4] may require prohibitive computational times, up to $120$s.

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In this work, we propose a fast superpixel-based color transfer method (SCT) that produces accurate color transfer between two images. Superpixels enable to lower the image dimension and to extract a reduced set of color candidates. We propose to use a fast approximate nearest neighbor matching algorithm in which we enforce the match diversity by limiting the selection of the same superpixels. A fusion framework is then designed to transfer the matched colors and we demonstrate the visual quality improvement obtained over exact nearest neighbor matching results. Finally, we show that the color transfer results of SCT are more visually satisfying or equivalent to the ones of state-of-the-art methods.

4 Conclusion

In this work, we propose a novel superpixel-based method for color transfer. Our algorithm is based on a fast ANN search and fusion of source colors in a non-local means framework. We introduce a method to constraint the neighbors diversity in the matching process, to get a large color palette of source superpixels. The colors are globally transfered to the target image with respect to the initial grain and exposure, producing visually consistent results. Finally, the use of superpixels within our framework enables to produce color transfer in very limited computational time. Future works will focus on the adaptation to video color transfer using supervoxels.