6.Spatial-Depth Super Resolution for Range Images

框架

[1]对low-resolution进行上采样，得到大小与原图一样大小的high-resolution 记作：D(0).
[2]迭代模块:基于当前深度图D(i)建立costVolume: Ci.
[3]在costVolume的每个切片中执行双边滤波以产生新的costVolume
[4]D(i+1):基于该costVolume首先选择具有最小成本的深度假设和之后的子像素估计.

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1.Construction and refinement of the cost volume

选择平方差作为成本函数，因为我们稍后将使用二次多项式插值用于子像素估计。 该成本函数可以帮助保持输入深度图的子像素精度。

可以通过颜色信息，获得立体空间超分辨率的锐利/真实深度边缘，接下来采用BF:

y, x are the indices of the current pixel in the camera image,
and u, v are two variables.γc and γs are two constants used as the thresholds of the color difference and the filter size.

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2.Sub-pixel Estimation

为了减少由深度假设选择过程中的量化引起的不连续性，基于二次多项式插值提出了子像素估计算法。

d is the discrete depth with the minimal cost
d_ = d − 1, and d+ = d + 1.
Xmin的估计值为上式

matlab code:

function Result = LayeredBilateralFilter(color,depth,sigma_w,sigma_c,w,DepthInteval,IterativeTime)
%% Initialization
L=10000;
k=1;
D(:,:,1) = double(depth);
CandidateD = 0:DepthInteval:255;
height = size(color,1);
width = size(color,2);
color = double(color);
CostVolume=zeros(height,width,length(CandidateD));
CostCW=zeros(height,width,length(CandidateD));

%% Iterative Module
while 1
    for i=1:length(CandidateD)
        CostVolume(:,:,i) = min(L,(CandidateD(i)-D(:,:,k)).^2);                   %Cost Volume C(i)
        CostCW(:,:,i) = BilateralFilter(color,CostVolume(:,:,i),sigma_w,sigma_c,w);   %A bilateral filtering is performed throughout each slice of the cost volume to produce the new cost volume 
        % Compare with the reference, the color space is different  
    end
    [BestCost,BestDepthLocation] = min(CostCW,[],3);                          %Selecting the depth hypothesis with the minimal cost

    % Sub-pixel estimation
    CostUpper = zeros(height,width);
    CostLower = zeros(height,width);
    for i = 1:length(CandidateD) 
        CostUpper = CostUpper + CostCW(:,:,i).*((BestDepthLocation+1)==i);
        CostLower = CostLower + CostCW(:,:,i).*((BestDepthLocation-1)==i);
    end
    k = k + 1;
    D(:,:,k) = CandidateD(BestDepthLocation) - DepthInteval * (CostUpper-CostLower) ./ (2*(CostUpper+CostLower-2*BestCost));  
    % end of sub-pixel estimation   

    if IterativeTime==k
        break;
    end
end
Result = D(:,:,IterativeTime);
end

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