K-nearest Neighbors Bilateral Interpolation (KBI)

• The paper introduces KBI as a local color correction component within a hybrid framework, utilizing bilateral weighting to adjust RGB channels based on geometric and color similarity.
• It computes a normalized weighted average per channel after filtering neighbors by CIELAB color differences, integrating spatial proximity and color similarity via Gaussian weights.
• Empirical ablation studies show improved color consistency with CMD of 8.095 and CPSNR of 29.413, demonstrating KBI’s effectiveness over standard KNN and global correction methods.

K-nearest Neighbors Based Bilateral Interpolation (KBI) is the local color-correction component of the grouping-based hybrid algorithm introduced in "A Novel Grouping-Based Hybrid Color Correction Algorithm for Color Point Clouds" for color consistency correction of aligned color point clouds (Chung et al., 4 Nov 2025). It is applied after registration, when a source point cloud and a target point cloud are already aligned but may still exhibit luminance/chrominance inconsistency due to exposure, white balance, lighting, angle, and related acquisition differences. KBI is designed for target points in the close proximity group $G^{cl}$, where local aligned source points are considered sufficiently trustworthy to support local correction. Its defining characteristic is a bilateral weighting rule in which each source neighbor is weighted jointly by geometric proximity and color similarity rather than by plain nearest-neighbor replacement or uniform $K$-neighbor averaging.

1. Placement in the hybrid correction framework

In the parent framework, the source and target point clouds are first aligned, after which the algorithm estimates the overlap rate between the aligned source cloud $P^{s,ali}$ and the target cloud $P^t$, partitions target points into proximity-based groups, and applies different correction mechanisms by group (Chung et al., 4 Nov 2025). Algorithm 1 assigns KBI to $G^{cl}$, JKHE (joint KBI + histogram equalization) to $G^{mod}$, and HE to $G^{dist}$.

The framework uses the estimated overlap rate $R$ to decide between a bi-group and a tri-group partition. A target point votes as overlapping if the distance to the aligned source cloud is below $T_d$, and after accumulating votes $V$, the overlap rate is

$K$0

The paper sets the overlap threshold $K$1 and the distance threshold $K$2 meter. If $K$3, the target cloud is partitioned into two groups, $K$4 and $K$5. If $K$6, it is partitioned into three groups, $K$7, $K$8, and $K$9. These groups are defined by the distance between each target point and its nearest aligned source point.

KBI is specifically assigned to $P^{s,ali}$0 because each target point $P^{s,ali}$1 in that group is relatively close to its nearest aligned source point, so local aligned source points can provide trustworthy local color-difference information. The same local mechanism is reused inside JKHE for $P^{s,ali}$2, where it is combined with a global histogram equalization term. By contrast, $P^{s,ali}$3 is corrected by HE only, reflecting the framework’s assumption that local source support becomes unreliable as proximity decreases.

2. Formal definition and notation

For a target point $P^{s,ali}$4, KBI first defines a geometry-based neighborhood

$P^{s,ali}$5

the set of the $P^{s,ali}$6-nearest aligned source points of $P^{s,ali}$7 in $P^{s,ali}$8 (Chung et al., 4 Nov 2025). The method does not use all $P^{s,ali}$9 neighbors blindly. It removes invalid aligned source points using a CIELAB color difference constraint: if the LAB color difference between $P^t$0 and a reference aligned source point $P^t$1 is larger than a specified threshold, that aligned source point is deleted. The surviving set is denoted

$P^t$2

For each color channel $P^t$3, the paper defines the channel-wise color difference

$P^t$4

where $P^t$5, $P^t$6 is the $P^t$7-channel value of the aligned source neighbor, and $P^t$8 is the $P^t$9-channel value of the target point.

The corrected $G^{cl}$0-channel is expressed as an additive update,

$G^{cl}$1

with

$G^{cl}$2

The paper’s printed equation has formatting corruption, but the normalized weighted-average interpretation is clearly intended and consistent with the notation.

The bilateral weight for each valid neighbor $G^{cl}$3 is

$G^{cl}$4

where $G^{cl}$5 denotes the Euclidean distance between target point $G^{cl}$6 and source reference point $G^{cl}$7, $G^{cl}$8 is the distance deviation, and $G^{cl}$9 is the color-difference deviation. KBI is therefore channel-wise: the correction is defined independently for $G^{mod}$0, $G^{mod}$1, and $G^{mod}$2, rather than via a single vector-valued formula.

3. Operational procedure and implementation details

For a target point $G^{mod}$3, the KBI procedure requires the aligned source point cloud $G^{mod}$4, the target cloud $G^{mod}$5, point coordinates for Euclidean nearest-neighbor search, RGB colors for source and target, the group assignment indicating $G^{mod}$6, the parameter $G^{mod}$7, the LAB color-difference threshold for valid-neighbor screening, and the Gaussian bandwidths $G^{mod}$8 and $G^{mod}$9 (Chung et al., 4 Nov 2025).

The workflow is explicit. First, the algorithm finds the $G^{dist}$0-nearest aligned source points of $G^{dist}$1 in geometry space, producing $G^{dist}$2. Second, it filters this set by CIELAB color difference, removing neighbors whose LAB difference from $G^{dist}$3 exceeds the specified threshold; the remaining valid set is $G^{dist}$4. Third, for each valid neighbor and each channel $G^{dist}$5, it computes $G^{dist}$6. Fourth, it computes the bilateral weight $G^{dist}$7 for each valid neighbor. Fifth, it evaluates the normalized weighted average $G^{dist}$8. Sixth, it updates the target color by adding that correction to the original target value. The process is repeated for all target points in $G^{dist}$9.

Several implementation constraints are explicit. Nearest neighbors are searched in the aligned source cloud and are defined as $R$0-nearest aligned source points after registration. The color-based restriction is not part of the neighbor search; it is a subsequent filtering step. Correction is performed per RGB channel, while the validity screening is performed in CIELAB space. The KBI term is normalized by $R$1, so the method is inherently a normalized weighted average rather than an unnormalized accumulation.

For KBI specifically, the provided text names but does not numerically specify the following parameters: $R$2, the LAB color-difference threshold, $R$3, and $R$4. The text also does not state how an empty valid-neighbor set $R$5 is handled if all $R$6 neighbors are rejected, or how extremely small denominators are stabilized. A plausible implication is that any implementation must provide a fallback for such cases, but that handling is not explicit in the provided material. The paper provides C++ source code for the full algorithm through the authors’ repository (Chung et al., 4 Nov 2025).

4. Bilateral character and methodological distinctions

KBI is termed bilateral interpolation because its interpolation weights combine two forms of similarity (Chung et al., 4 Nov 2025). The first factor,

$R$7

is a spatial Gaussian that favors source points geometrically close to the target point. The second factor,

$R$8

is a range or color Gaussian that favors source points whose color is already similar to the target color in the corresponding channel. This structure is directly analogous in spirit to bilateral filtering, with one kernel acting in the domain and the other in the range.

The paper distinguishes KBI from ordinary $R$9-nearest-neighbor averaging in several ways. KBI does not use uniform weights, does not average source colors directly, and does not trust all $T_d$0 neighbors equally. Instead, it computes a normalized weighted average of source-target color differences, and it removes invalid neighbors using a CIELAB threshold before interpolation. Relative to inverse-distance interpolation, KBI adds a color-similarity term, so a geometrically close but color-inconsistent source point receives lower influence. Relative to standard bilateral filtering, KBI operates in an irregular point-cloud correspondence setting: source and target are different point sets, the neighborhood is formed from aligned source points around a target point, and the output is a cross-cloud color correction estimate rather than a same-signal smoothing result.

The method’s role is therefore more specific than generic smoothing. It is a local transfer mechanism that estimates an additive color offset from valid local aligned source points and applies that offset only where local source support is considered reliable.

5. Empirical evidence, ablation, and boundary behavior

The parent paper reports that the desired color consistency correction benefit of the full algorithm is justified through 1086 testing color point cloud pairs against state-of-the-art methods (Chung et al., 4 Nov 2025). KBI is not presented in isolation with a standalone results table, but the ablation studies identify its contribution within the grouped design.

The key evidence is Table 6, which compares different assignments of KBI, JKHE, and HE across the proximity groups. The proposed assignment—KBI for $T_d$1, JKHE for $T_d$2, and HE for $T_d$3—achieves the best reported combination among the listed variants, with CMD $T_d$4 and CPSNR $T_d$5. This supports the framework’s design claim that KBI is most effective where local geometry support is strongest, while JKHE is preferable for moderate proximity and HE is reserved for distant points.

Configuration	CMD	CPSNR
Bi-group: KBI for $T_d$6 and $T_d$7; Tri-group: KBI for $T_d$8, $T_d$9, HE for $V$0	12.201	28.488
Bi-group: JKHE for $V$1 and $V$2; Tri-group: JKHE for $V$3, $V$4, HE for $V$5	11.997	23.074
Proposed algorithm: KBI for $V$6, JKHE for $V$7, HE for $V$8	8.095	29.413

The qualitative discussion in the paper further attributes improved local behavior to KBI in $V$9 and to the KBI term inside JKHE for $K$00. The paper states that NN and KNN fail in occluded or global-shift regions because they lack global correction, whereas HM, AGL, and HHM fail in locally detailed or noisy regions because they lack local reference consideration. The proposed method is described as performing well in both kinds of areas, including noisy local portions, shadows, gloves, brick textures, wall corners, and plant regions. This suggests that KBI is intended as the detail-preserving local engine within the hybrid framework, rather than as a universal correction rule for all target points.

KBI also enters the paper’s grouping-effect free argument. At the $K$01/$K$02 boundary, for the leftmost point $K$03 in $K$04, the JKHE weights become

$K$05

so that

$K$06

The first point in $K$07 is therefore corrected purely by KBI, matching the method used for the last point in $K$08, which prevents a correction discontinuity across that boundary. The framework also implicitly identifies a limitation of KBI: when local source support becomes only moderate or distant, KBI alone is insufficient, motivating JKHE and HE.

6. Relation to neighboring nearest-neighbor interpolation research

KBI is a specific point-cloud color-correction method rather than a general theory of nearest-neighbor interpolation, but two adjacent lines of work help situate its design. "Benefit of Interpolation in Nearest Neighbor Algorithms" studies interpolated nearest-neighbor weighting schemes in classification and regression, not bilateral interpolation in the image-processing sense (Xing et al., 2022). Its central result is that a mild degree of interpolation via distance-dependent weights can strictly improve prediction performance and statistical stability over ordinary $K$09-NN, while extreme interpolation trends toward 1-NN behavior and produces a U-shaped performance curve. This suggests a useful conceptual backdrop for KBI’s nonuniform local weighting: emphasizing nearby neighbors can be beneficial, but the paper does not address bilateral weights that jointly depend on geometric distance and color similarity.

A different structural comparison is provided by "Spherical k-Nearest Neighbors Interpolation," which introduces SkNNI and the NDDNISD interpolation rule for scalar geospatial interpolation on the sphere (Trempe, 2019). That method combines query-neighbor proximity with a second factor derived from neighborhood distribution, yielding a dual-factor weighting rule that is KNN-based and interpolation-oriented, but not bilateral in the classical sense because it does not use feature or value similarity. Relative to that design, KBI is closer to the classical bilateral paradigm because its second factor is explicitly a color-similarity term.

Taken together, these neighboring works indicate that KBI belongs to a broader family of weighted nearest-neighbor interpolators while remaining methodologically distinct. Its defining specialization is the use of aligned source-target geometry, CIELAB-based validity screening, and bilateral weights over Euclidean proximity and channel-wise color difference for local color consistency correction of point clouds (Chung et al., 4 Nov 2025).