Table 1.

The notation of the used parameters and functions.

Section	Parameters or Functions	Descriptions
	$E\left(f\right)$	Energy function to generate color-flattening, $E\left(f\right)=e_d+E_p$.
	$E_d$	Data term of energy function for pixel-wise intrinsic similarity.
	$z^{\ast }$	A concatenated vector of all pixel values in transformed image $I_c$.
	z	A concatenated vector of all pixel values in original image I.
4.1	$E_p$	Smoothness term of energy function.
	$x_i$	A 3-dimensional vector of the RGB values at pixel position $p_i$ of transformed image $I_c$.
	${\omega }_{i,j}$	Weights to the difference between $x_i$ of pixel position $p_i$ and $x_j$ of the neighboring pixel $p_j$ of $p_i$.
	$f_i$	A 3-dimensional vector of the CIELab color space of $p_i$.
	κ	A constant related to the luminance variations.
	M	The $m_l\times n$ matrix consists of ${\omega }_{i,j}$ and $-{\omega }_{i,j}$.
	$d_k$ and $b_k$	Intermediate variables of the split Bregman method.
	${\gamma }_i$	${\gamma }_i=[x_i,y_i,z_i]$, the i-th 3D point data of 3D point clouds.
4.2	${\Gamma }_i$	The i-th voxel includes the reflected particles with a size of $m_v^x\times m_v^y\times m_v^z$.
	$N_{\Gamma }$	The number of voxels in a 3D point cloud.
	${\Gamma }_i^{max}$	The possible number of reflectance particles in voxel ${\Gamma }_i$.
	$\mathcal{S}$	A set of segmented partition of the color-flatted image.
	$N_s$	The number of segmented partitions.
	$\mathcal{N}\left(s_i\right)$	Set of spatially-connected neighborhood partitions of the $s_i$ partition.
	${\psi }_{i,j}$	The dissimilarity function to group the adjacent partitions.
	${\psi }_{i,j}^c$	${\psi }_{i,j}^c=\left|\right|z_i^c-z_j^c{\left|\right|}_1$; the color dissimilarity between the adjacent partitions.
	${\alpha }_c$	A weight constant for the color dissimilarity.
5.1	$z^c$	75-bin color histogram measured from the mean image $I_{\mu }$.
	${\psi }_{i,j}^t$	The texture dissimilarity between the adjacent partitions.
	${\alpha }_t$	A weight constant for the texture dissimilarity.
	$z^t$	240-bin SIFT histogram of original image I.
	${\theta }_d$	A threshold value for grouping adjacent partitions.
	S and $S^{\prime }$	The ground truth of the segmented and inferred segmentation images from the proposed method.
	$N_s$	The number of training images to find $\alpha =[{\alpha }_c,{\alpha }_t]$.
	$\Delta (·,·)$	The structural loss between the ground truth and the inferred segmented partition.
	${\alpha }_{i,i\in n}$	The classification results of each bounding box provided from the image.
6.2	${\beta }_{j,j\in m}$	The classification results of each bounding box provided from the 3D point clouds.
	$m_{{\alpha }_i,{\beta }_j}$	The association component between ${\alpha }_i$ and ${\beta }_j$.