Four-Dimensional Hyperspectral Imaging for Fruit and Vegetable Grading

Abstract

Reliable, non-destructive grading of fresh fruit requires simultaneous assessment of external morphology and hidden internal defects. Camera-based grading of fresh fruit using colorimetric (RGB) and near-infrared (NIR) imaging often misses subsurface bruising and cannot capture the fruit’s true shape, leading to inconsistent quality assessment and increased waste. To address this, we developed a 4D-grading pipeline that fuses visible and near-infrared (VNIR) and short-wave infrared (SWIR) hyperspectral imaging with structured-light 3D scanning to non-destructively evaluate both internal defects and external form. Our contributions are (1) flagging the defects in fruits based on the reflectance information, (2) accurate shape and defect measurement based on the 3D data of fruits, and (3) an interpretable, decision-tree framework that assigns USDA-style quality (Premium, Grade 1/2, Reject) and size (Small–Extra Large) labels. We demonstrate this approach through preliminary results, suggesting that 4D hyperspectral imaging may offer advantages over single-modality methods by providing clear, interpretable decision rules and the potential for adaptation to other produce types.

1. Introduction

Reliable grading must detect both obvious blemishes and hidden internal flaws such as bruises, early decay, or cell damage that elude human inspectors and standard colorimetric (RGB) and near-infrared (NIR) cameras. Left undetected, these hidden defects not only shorten shelf life and increase waste but can also trigger costly recalls and erode consumer trust. A truly robust solution must non-destructively detect internal injuries and measure a fruit’s external form, ensuring only structurally sound, blemish-free produce moves through the supply chain and meets stringent regulatory and buyer standards. However, today’s automated approaches typically rely on manual inspection or simple RGB/NIR imaging systems, which, despite being faster than purely human checks, remain subjective and surface-bound, often missing subsurface damage entirely.

Automated machine-vision and deep-learning (DL) grading pipelines have been developed for a wide variety of fruits and have demonstrated the ability to non-destructively sort produce by external traits (shape, color, size, surface defects) and proxies for internal quality (sweetness, firmness) with over 90% accuracy. In apple grading, early mechanical systems and sensor-based methods extracted features such as geometry, color, and firmness to categorize cultivars and detect bruises [1,2,3,4]. More recently, convolutional neural networks on RGB images—employing one-stage detectors (YOLOv5, YOLOv4) for blemish segmentation and classification networks (AlexNet, VGG variants) for final grade assignment—have further improved speed and accuracy on benchmark datasets [5,6,7,8,9]. Parallel efforts in tomato grading have combined shape (eccentricity), size (2D area), color (mean RGB), and contour analyses, via online sorting rigs, maturity classifiers, and dual-view frameworks, to achieve similar high-throughput performance [10,11,12]. Despite these successes, all RGB+DL approaches remain limited to surface inspection and 2D morphology, missing subsurface defects and true three-dimensional shape. In addition, the black-box nature of deep learning models often limits their interpretability, posing challenges for trust, traceability, and adoption in agricultural grading tasks [13,14].

Hyperspectral imaging (HSI) directly addresses these surface-only blind spots by capturing a continuous reflectance spectrum at every pixel, revealing the chemical and structural signatures of subsurface bruising and early decay that RGB+DL pipelines miss. For instance, in apples, visible and near-infrared (VNIR)/short-wave infrared (SWIR) HSI combined with multivariate analyses (PLS, PCA) and optimized classifiers (GS-SVM, GA-SVM) has discriminated bruise severity and even age with accuracies often exceeding 90% [15,16,17]. In tomatoes, VIS/NIR HSI with ant-colony-optimized wavelength selection and PLS-DA/ANN models has classified simulated bruise levels at up to 100% accuracy while reducing spectral variables by more than 70% [18]; multivariate classifiers detect early decay before any visual sign with over 90% accuracy [19]; and SEM-validated studies show bruised regions exhibit reflectance drops near 810 nm, yielding 90.9% PLS-DA performance [20]. However, HSI alone lacks direct 3D localization and cannot measure true bruise dimensions or overall fruit geometry, metrics that, together with size and roundness, underpin USDA-style grading. Additionally, because HSI alone lacks depth cues, it can struggle to interpret complex shapes or shadowed regions with high accuracy. In such cases, systems often need to combine HSI with external geometric information or rely on complex 2D image processing steps to approximate shape and size, which can introduce errors [21].

Beyond RGB-based and hyperspectral imaging, 3D-sensing methods such as stereo vision and time-of-flight (ToF) sensors have also been used in agriculture for fruit grading and plant phenotyping [22,23]. However, stereo vision depends heavily on surface texture, making it unreliable for the smooth, uniform surfaces of many fruits, while ToF sensors often lack the spatial resolution needed for fine geometric measurements and can struggle with shadows, occlusions, and high-speed sorting. Fringe Projection Profilometry (FPP) addresses many of these limitations by projecting structured light patterns independent of surface texture, enabling robust, sub-millimeter-accurate 3D reconstruction [24]. With its ability to rapidly capture full fruit geometry in a single scan, FPP may represent a more precise and high-throughput alternative for fruit grading applications.

In this paper, we introduce a unified 4D-grading system that integrates VNIR/SWIR hyperspectral imaging with high-resolution 3D scanning to deliver fully non-destructive and objective assessment of both internal and external quality attributes for spherical fruits. Our unified 4D-grading pipeline begins by reconstructing each fruit’s surface mesh in MATLAB to extract the two equatorial diameters and height, which are then sorted into $a \ge b \ge c$ to compute Mohsenin’s sphericity index (see Section 3.1). Next, we calculate the spectral-difference defect flag from VNIR and SWIR reflectance cubes to identify subsurface bruising (see Section 2.3). Fruits flagged as defective proceed down the Defect branch, where measured bruise length and sphericity determine Grade 1, Grade 2, or Reject, while non-defective specimens follow the Non-Defective branch and are graded solely by sphericity. In parallel, the longest span a is compared against USDA size bins to assign Small through Extra Large (see Section 4). Finally, quality and size classes are concatenated into a single grade. We demonstrate our method on a small set of apple and tomato samples, indicating that 4D fusion has the potential to complement single-modality techniques by improving early defect detection, while remaining compatible with real-time automated packing lines.

2. Materials and Methods

2.1. Four-Dimensional Hyperspectral Imaging System

We developed a 4D hyperspectral imaging system [25] capable of simultaneously acquiring the 3D geometric structure and hyperspectral reflectance information of objects, as illustrated in Figure 1. The system comprises two main subsystems: a hyperspectral imaging subsystem and a 3D imaging subsystem. The 3D imaging subsystem is based on a conventional fringe projection profilometry (FPP) setup, which includes a digital projector (DLPLCR4500LVM, Texas Instruments, Dallas, TX, USA) and a camera (Grasshopper3 Monochrome GS3-U3-41C6M-C, FLIR, Wilsonville, OR, USA). The hyperspectral imaging subsystem consists of two components: a VNIR camera (Grasshopper3 Monochrome GS3-U3-23S6M-C, FLIR, Wilsonville, OR, USA) coupled with a VNIR spectrograph (ImSpector V10, Specim, Oulu, FL, USA) and an SWIR camera (Xenicas Xeva 18544, Leuven, Belgium paired with an SWIR spectrograph (ImSpector N17E, Specim, Oulu, FL, USA). Together, these components enable the acquisition of hyperspectral images across a broad spectral range, spanning from 400 nm to 1700 nm. To achieve accurate spatial alignment between the geometric and spectral data, we employed the line-scan homography method proposed in [25] to achieve registration between the 3D data and the corresponding hyperspectral images with subpixel accuracy.

2.2. Three-Dimensional Geometry Acquisition Through Fringe Projection Profilometry

The 3D geometry for each of the fruits is extracted using fringe projection profilometry, a structured-light-based 3D vision technique. As detailed in Section 2.1, this involves a calibrated camera–projector setup, with the camera capturing images of sinusoidal fringe patterns projected on the object (which in our case is the fruit or vegetable in question) at known phase shifts. This is calibrated according to the technique described in Li et al. [26]. A schematic of this is shown in Figure 2. The camera and projector are both modeled according to the pinhole model. This is described by the following equations:

$$s_c{I}_c=A_c[R_c,t_c]X_w,$$

(1)

$$s_p{I}_p=A_p[R_p,t_p]X_w,$$

(2)

where $s_c$ and $s_p$ describe the scaling factors; $I_c$ and $I_p$ describe the coordinates; $A_c$ and $A_p$ describe the intrinsic matrices; and $[R_c, t_c]$ and $[R_p, t_p]$ describe the extrinsic matrices of the camera and projector, respectively. $X_w={[x_w, y_w, z_w, 1]}^T$ is the object point in the world coordinate system.

To extract the 3D coordinates of object points, it is essential to compute the phase information of the projected sinusoidal fringe patterns, which serves as a critical bridge for establishing a correspondence between camera pixels and projector pixels. Specifically, a sequence of sinusoidal fringe patterns $I_k$ with equal and known phase shifts between adjacent patterns is projected onto the object as follows:

$$I_k=I_{int}+I_{mod}\left[cos(\varphi +{\displaystyle \frac{2\pi k}{N}})\right]$$

(3)

Here, $I_{int}$ refers to the background intensity, $I_{mod}$ means the intensity modulation, N is the number of phase shifting steps, and $\varphi$ is the phase to be solved for. After capturing these fringe images, a wrapped phase map can be computed as

$$\varphi =-arctan({\displaystyle \frac{{\sum }_{k=1}^N{I}_{k}sin{\theta }_k}{{\sum }_{k=1}^N{I}_{k}cos{\theta }_k}})$$

(4)

Given the nature of arctangent function, the wrapped phase has $2\pi$ discontinuities; therefore, these $2\pi$ discontinuities must be removed to obtain an absolute phase map before it can be utilized for 3D coordinate computation.

$$\Phi =\varphi +k\times 2\pi .$$

(5)

Once the absolute phase is computed, the camera and projector image points can be correlated as follows:

$${\Phi }_a^c(u^c,v^c)={\Phi }_a^p\left(u^p\right)=\Phi$$

(6)

Here, the camera pixel coordinates are represented by $(u^c, v^c)$ and the projector pixel coordinates are represented by $(u^p,v^p)$. ${\Phi }_a^c$ is the absolute phase of each camera pixel and ${\Phi }_a^p$ is the absolute phase of each projector pixel.

$$u^p={\displaystyle \frac{\Phi \times P+\pi W^p}{2\pi }}$$

(7)

From the equations defined above and the original calibration Equations (1) and (2), we get the object coordinates in the world coordinate system [27].

$$\left[\begin{array}{c}x\\ y\\ z\end{array}\right]={\left[\begin{array}{ccc}{a}_{11}^c-u^c{a}_{31}^c& a_{12}^c-u^c{a}_{32}^c& a_{13}^c-u^c{a}_{33}^c\\ a_{21}^c-v^c{a}_{31}^c& a_{22}^c-v^c{a}_{32}^c& a_{23}^c-v^c{a}_{33}^c\\ a_{11}^p-u^p{a}_{31}^p& a_{12}^p-u^p{a}_{32}^p& a_{13}^p-u^p{a}_{33}^p\end{array}\right]}^{-1}\left[\begin{array}{c}{u}^c{a}_{34}^c-a_{14}^c\\ v^c{a}_{34}^c-a_{24}^c\\ u^p{a}_{34}^p-a_{14}^p\end{array}\right]$$

(8)

where $a_{ij}^c$ represents the constituent elements of camera intrinsic matrix $A_c$ and $a_{ij}^p$ represents the constituent elements of projector intrinsic matrix $A_p$. These coordinates can be used to calculate diameter, bruise length, and other shape parameters that may be used as inputs to a grading algorithm.

2.3. Spectral Reflectance from Hyperspectral Data

Hyperspectral imaging (HSI) captures reflectance at dozens or even hundreds of narrow wavelengths, revealing subtle chemical and structural changes that occur when fruit tissue is bruised or decaying. Unlike standard RGB or single-band NIR cameras, HSI can distinguish healthy versus defective areas based on their unique spectral fingerprints across the VNIR and SWIR regions. In this study, we use VNIR (400–1000 nm) and SWIR (1000–1700 nm) cubes to segment defect pixels by comparing their average spectra to healthy tissue.

Prior work has shown that spectral-reflectance contrasts reliably indicate bruising. Lu et al. [28] used NIR HSI to distinguish subsurface apple bruises, and Tan et al. [29] applied VNIR/SVM for high-accuracy severity grading. Baranowski et al. [30] tracked VNIR/SWIR changes to predict bruise age with over 90% accuracy. In tomatoes, PLS-DA models detected impact bruises at 90.9% accuracy [20], chemometric band selection isolated defect wavelengths [31], and interval-optimized PLS-DA/ANN classifiers reached up to 100% severity accuracy with 70% fewer bands [18]. Building on these findings, we selected a spectral-difference threshold of $d_{\mathrm{Spec}} \ge 0.02$ to flag tissue anomalies. This choice was guided by prior studies that quantified reflectance contrasts between bruised and healthy fruit regions. In Lu et al.’s work on apples [28], the spectral difference between healthy and bruised tissue typically ranged from 0.02 to 0.17. ElMasry et al. [17] observed approximately a 5% reflectance difference between bruised and unbruised areas in green apples. For tomatoes, Sun et al. [20] reported an average difference of 10% between healthy and bruised tissue. Although our 2% threshold is more conservative than these reported values, it provides a robust lower bound for detecting subtle defects within our small dataset and serves as a reliable starting point for future tuning.

To obtain reflectance data, we first convert the raw VNIR and SWIR image stacks into calibrated reflectance cubes via dark–white normalization:

$$R(x,y,\lambda )={\displaystyle \frac{I(x,y,\lambda )-D(x,y,\lambda )}{max\left[W(x,y,\lambda )-D(x,y,\lambda ),\epsilon \right]}},$$

(9)

clamping $R\in [0, 1]$. After selecting the fruit region of interest (ROI), we reshape the valid spectra into a 2D array and apply PCA. We extract only the first principal-component image because this single grayscale map maximizes variance due to bruised or decayed tissue, and delineate defect pixels via manual annotation to form a binary mask $\mathcal{M}$.

From $\mathcal{M}$ and its complement we compute the average reflectance spectra in both VNIR and SWIR:

$${\overline{R}}_{\mathrm{def}}\left(\lambda \right)={\displaystyle \frac{1}{\left|\mathcal{M}\right|}}\sum _{(x,y)\in \mathcal{M}}R(x,y,\lambda ),{\overline{R}}_{\mathrm{hea}}\left(\lambda \right)={\displaystyle \frac{1}{|\mathcal{F}\setminus \mathcal{M}|}}\sum _{(x,y)\in \mathcal{F}\setminus \mathcal{M}}R(x,y,\lambda ).$$

(10)

We then reduce each spectral region to a single scalar

$$\begin{array}{cc}\hfill d_{\mathrm{VNIR}}& =\underset{\lambda }{max}|{\overline{R}}_{\mathrm{def}}^{\mathrm{VNIR}}\left(\lambda \right)-{\overline{R}}_{\mathrm{hea}}^{\mathrm{VNIR}}\left(\lambda \right)|,\hfill \end{array}$$

(11)

$$\begin{array}{cc}\hfill d_{\mathrm{SWIR}}& =\underset{\lambda }{max}\left|{\overline{R}}_{\mathrm{def}}^{\mathrm{SWIR}}\left(\lambda \right)-{\overline{R}}_{\mathrm{hea}}^{\mathrm{SWIR}}\left(\lambda \right)\right|.\hfill \end{array}$$

(12)

and define the overall spectral difference as

$$d_{\mathrm{Spec}}=max\left\{d_{\mathrm{VNIR}},d_{\mathrm{SWIR}}\right\}.$$

(13)

where

• $I(x, y, \lambda )$ is the raw image intensity at pixel $(x, y)$ and wavelength $\lambda$;
• $D(x, y, \lambda )$ is the dark-reference image;
• $W(x, y, \lambda )$ is the white-reference image;
• $\epsilon$ is a small constant to avoid division by zero;
• $R(x, y, \lambda )$ is the calibrated reflectance;
• $\mathcal{M}$ is the defect mask over the fruit ROI;
• $\mathcal{F}$ is the set of all fruit ROI pixels;
• $d_{\mathrm{VNIR}}$ is the VNIR spectral difference (Equation (11));
• $d_{\mathrm{SWIR}}$ is the SWIR spectral difference (Equation (12));
• $d_{\mathrm{Spec}}$ is the overall spectral-difference flag.

Figure 3 illustrates, for apples, the mean reflectance curves of defective (red) vs. healthy (green) apple tissue in Figure 3a the VNIR bands and Figure 3b the SWIR bands. Similarly, Figure 4 shows the reflectance curves of defective (red) vs. healthy (green) tomato tissue in Figure 4a the VNIR bands and Figure 4b the SWIR bands. Since there is a clear distinction between the reflectance values of the defective and healthy tissues for both apple and tomato examples, we chose to leverage this difference in reflectance values to differentiate between the healthy and damaged fruits.

3. Parameters for Fruit Grading from 4D Hyperspectral Data

Our 4D-grading pipeline relies on two fundamental parameter sets: shape parameters obtained from 3D-mesh reconstruction (Section 3.1), and defect parameters derived from VNIR/SWIR hyperspectral analysis (Section 3.2). Together, these metrics directly inform the subsequent decision-tree grading logic.

3.1. Shape Characterization Using 3D Data

Shape characterization begins by capturing a dense 3D point cloud of each fruit using a structured-light scanner. As outlined in Section 2.2, our 3D-scanning setup produces a high-resolution point cloud, yielding precise $(X, Y, Z)$ coordinates across the entire surface. From this data, we reconstruct a continuous surface mesh in MATLAB (R2025a), enabling direct measurement of geometric traits such as diameters and height.

To extract each measurement, we display the mesh in MATLAB and manually pick two equatorial points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ (for the diameters $D_1$ and $D_2$), plus a top point $(x_T, y_T, z_T)$ and bottom point $(x_B, y_B, z_B)$ (for height H). Each span is computed by

$$\begin{array}{cc}\hfill D& =\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2+{(z_2-z_1)}^2},\hfill \end{array}$$

(14)

$$\begin{array}{cc}\hfill H& =z_T-z_B.\hfill \end{array}$$

(15)

Given the two equatorial diameters $D_1, D_2$ and height H, we sort the set $\{D_1, D_2, H\}$ in descending order to assign

$$a=max\{D_1, D_2, H\},b=\mathrm{median}\{D_1, D_2, H\},c=min\{D_1, D_2, H\}.$$

Substituting these into Mohsenin’s sphericity formula [32]

$$\Phi ={\displaystyle \frac{{\left(abc\right)}^{1/3}}{a}}$$

(16)

ensures that a is always the longest span, b the intermediate, and c the shortest. Figure 5 illustrates this workflow, showing both the raw structured-light image captured during acquisition and the corresponding 3D mesh used for manual diameter measurements.

3.2. Defect Characterization Using Hyperspectral and 3D Data

Having extracted the key 3D shape metrics above, we now turn to defect detection by fusing VNIR and SWIR hyperspectral data with our mesh geometry. For each fruit, we compute the mean “defect” and “healthy” reflectance curves as in Equation (10), then reduce them to a single scalar in each band (Equations (11) and (12)) and determine $d_{\mathrm{Spec}}$ as defined in Equation (13).

According to our 4D decision tree (Section 4), any sample with $d_{\mathrm{Spec}} \ge 0.02$ (2%) or a manual VNIR/SWIR mask is routed into the Defective branch; the remainder proceed to the Non-Defective branch for size-only grading.

For fruits flagged as Defective, we project the binary mask onto the 3D mesh and manually pick two opposing points $(x_{b1}, y_{b1}, z_{b1})$ and $(x_{b2},y_{b2},z_{b2})$ on the bruise region. The bruise length $L_b$ is then computed via the same Euclidean-distance formula (Equation (14)). Figure 6 shows an example of this mesh-based measurement.

4. Fruit Grading Strategies

Having established our spectral-difference defect flag (Section 3.2) and 3D-shape measurement pipeline (Section 3.1), we now integrate these modalities into a unified decision-tree framework that assigns both quality and size grades. We adopt a decision-tree structure because it offers clear, interpretable rules at each node, mirrors the stepwise logical flow of human grading decisions, and allows simple tuning of numerical thresholds for different fruit types or market classes.

The use of sphericity as a geometric grading parameter is motivated by USDA shape standards, which assign higher quality grades to fruits that are “well formed” or “fairly well formed,” and penalize irregular or misshapen specimens [33]. Sphericity provides a clear and consistent way to measure how round a fruit is, making it a useful indicator of shape regularity. Prior studies have reported sphericity values ranging from 0.84 to 0.93 across four tomato cultivars [34], 0.82 to 1.00 in a sample of 100 tomatoes [35], and 0.86 to 0.98 across various apple cultivars [36]. These ranges align with the 80–100% values observed in our dataset. We therefore adopt sphericity-based thresholds in our 4D-grading system to reflect USDA shape expectations and trends in the prior literature. Building on these trends, we note that tomatoes also tend to be more spherical than apples in the literature and are visually more sensitive to shape deformities in the market; we therefore apply slightly stricter sphericity thresholds to tomatoes than apples in our pipeline. Moreover, in our decision framework, the combination of sphericity and bruise severity enables a tiered grading system: fruits with the highest sphericity and minimal bruising receive top grades, while those with lower sphericity and a greater extent of defects are assigned lower grades. This mirrors USDA logic, where the absence of shape deformities and physical damage corresponds to higher grade classifications, ensuring that our system mimics both the structure and intent of official grading standards.

Our unified 4D pipeline begins by reconstructing the fruit’s surface mesh (Section 3.1) and immediately extracting two key metrics: Mohsenin’s sphericity $\Phi$ as computed by Equation (16), which captures overall roundness, and the longest span a from the ordered set $\{D_1, D_2, H\}$, which underlies USDA size classification [33,37].

Next, we assess tissue integrity via the spectral-difference score as defined in Equation (13). Any fruit with a spectral difference $\ge 0.02$ is routed into the Defective branch; all others proceed as Non-Defective. Within the Non-Defective branch, quality is assigned solely on $\Phi$. Specimens with sphericity values exceeding defined thresholds are assigned Premium or Grade 1/2. In the Defective branch, we measure bruise length $L_b$ on the 3D mesh via Equation (14) and combine it with $\Phi$ according to the rules in Figure 7 for apples and Figure 8 for tomatoes to yield Grade 1, Grade 2, or Reject.

Finally, size class is determined by comparing the longest span a to USDA diameter bins (Small–Extra Large) and the fruit’s definitive label is formed by concatenating its quality grade and size class (e.g., “Grade 1 Large”). Figure 7 illustrates the full decision tree for apples and Figure 8 that for tomatoes.

Although we have demonstrated our 4D-grading pipeline on apples and tomatoes, the same approach can be applied to nearly any spherical fruit simply by tuning a few spectral-difference and geometric thresholds.

4.1. Apples

As shown in Figure 7, we first compute Mohsenin’s sphericity index $\Phi$ (Equation (16)) from the ordered principal spans $a \ge b \ge c$. We then evaluate the spectral-difference flag as defined in Equation (13). Any apple with $\Delta \ge 0.02$ (2%) or a manual VNIR/SWIR mask is routed into the Defective branch; all others follow the Non-Defective branch. Non-Defective Apples: Grading is based solely on sphericity $\Phi$ (

Table 1. Non-defective apple grading by sphericity $\Phi$.

Quality Grade	Sphericity $\mathbf{\Phi }$ (%)
Premium	$\Phi \ge 90$
Grade 1	$85\le \Phi <90$
Grade 2	$80\le \Phi <85$
Reject	$\Phi <80$

).

Defective Apples: We measure bruise length $L_b$ on the 3D mesh (via Equation (14)) and combine it with $\Phi$ to assign Grade 1, Grade 2, or Reject per

Table 2. Defective apple grading rules.

Condition	Assigned Grade
Minor bruise ($L_b\le 15.875\mathrm{mm}$) and $\Phi \ge 90\%$	Grade 1
Minor bruise and $85\%\le \Phi <90\%$	Grade 2
Moderate bruise ($15.875<L_b\le 22.225\mathrm{mm}$) and $\Phi \ge 85\%$	Grade 2
Otherwise	Reject

.

Size Classification: In both branches, we compare the longest span a against USDA apple size bins (

Table 3. USDA apple size classes by longest span a.

Size Class	a (mm)
Small	$a\le 60.3$
Medium	$60.3<a\le 63.5$
Large	$63.5<a\le 69.9$
Extra Large	$a>69.9$

) to assign Small through Extra Large.

The final apple label concatenates the quality grade (Premium/Grade 1/Grade 2/Reject) with the size class (Small/Medium/Large/Extra Large), e.g., “Grade 1 Large.” Figure 7 illustrates our apple grading decision tree.

4.2. Tomatoes

As shown in Figure 8, for each tomato, we first compute Mohsenin’s sphericity index $\Phi$ (Equation (16)) from the three sorted spans $a \ge b \ge c$. Similarly, we then evaluate the spectral-difference flag as defined in Equation (13).

Non-Defective: If $\Delta < 0.02$, grade by sphericity alone using

Table 4. Non-defective tomato grading by sphericity $\Phi$.

Quality Grade	Sphericity $\mathbf{\Phi }$ (%)
Premium	$\Phi \ge 95$
Grade 1	$90\le \Phi <95$
Grade 2	$80\le \Phi <90$
Reject	$\Phi <80$

.

Defective: If $\Delta \ge 0.02$, measure 3D bruise length $L_b$ via Equation (14) and combine with $\Phi$ as per

Table 5. Defective tomato grading rules.

Condition	Assigned Grade
$L_b\le 9.525$ mm and $\Phi \ge 90$%	Grade 1
$L_b\le 9.525$ mm and $80\%\le \Phi <90\%$	Grade 2
$9.525<L_b\le 15.875$ mm and $\Phi \ge 90$%	Grade 2
Otherwise	Reject

.

Finally, in both branches we compare the longest span a against USDA tomato size bins (

Table 6. USDA tomato size classes by longest span a.

Size Class	a (mm)
Small	$a\le 57.96$
Medium	$57.96<a\le 64.29$
Large	$64.29<a\le 70.62$
Extra Large	$a>70.62$

) and concatenate quality + size (e.g., “Grade 1 Large”). Figure 8 illustrates our tomato grading decision tree.

5. Results

Having established our 4D-grading pipeline for hyperspectral defect detection (Section 2.3), 3D shape measurement (Section 3.1), and decision-tree–based grading (Section 4), we now assess its performance on a set of representative fruits. In the subsections that follow, we apply the full 4D workflow to apples (Section 5.1) and tomatoes (Section 5.2), reporting for each specimen the computed spectral-difference flag, geometric spans and sphericity, bruise metrics (where applicable), and the final concatenated USDA-style grade. All experiments and data collection were conducted in July 2024. This evaluation was performed on a small exploratory dataset of five fruits (three apples and two tomatoes). Although it does not capture the full variability of cultivars and defect types, it demonstrates the technical feasibility of the proposed 4D-grading pipeline and lays the groundwork for future large-scale validation.

5.1. Apple Results

Table 7. Measured parameters and final grades for all apple samples.

Sample	Defective?	${\mathit{d}}_{\mathbf{Spec}}$	${\mathit{L}}_{\mathit{b}}$ (mm)	a / b / c (mm)	$\mathbf{\Phi }$ (%)	Size	Final Grade
Apple 1 (no defect)	No	—	—	69.30 / 62.19 / 60.08	91.97	Large	Premium Large
Apple 2 (no defect)	No	—	—	77.06 / 58.91 / 58.47	83.40	Large	Grade 2 Large
Apple 3 (defective)	Yes	0.035	12.4	76.18 / 65.71 / 63.21	89.45	Extra Large	Grade 2 Extra Large

summarizes the key 4D parameters and final grades for all three apples. Non-defective fruits report only sphericity $\Phi$ (no spectral flag or bruise measurement), while the one defective specimen also shows its spectral-difference score $d_{\mathrm{Spec}}$ and 3D bruise length $L_b$.

Here, $d_{\mathrm{Spec}}$ is the spectral-difference score (see Equation (13)), used to flag internal tissue defects; $L_b$ is the 3D measured bruise length on the surface mesh; $a, b, c$ denote the ordered principal spans of the fruit (longest to shortest); and $\Phi$ is Mohsenin’s sphericity index (Equation (16)).

As shown in Table 7, Apples 1 and 2 both fell below the $2\%$ spectral-difference threshold and were routed to the Non-Defective branch. Their sphericity values of $91.97\%$ and $83.40\%$ correspond to “Premium” and “Grade 2” under our sphericity-only grading rules. Apple 3, by contrast, registered a spectral-difference of $3.5\%$ and a bruise length of 12.4 mm, placing it in the Defective branch; its sphericity of $89.45\%$ and bruise-severity band then yield a “Grade 2” quality. All three apples fell into the Large or Extra Large USDA size classes, so their final labels concatenate quality and size (e.g., “Grade 2 Extra Large”). Figure 9 shows RGB images of the three apples discussed in Table 7, providing a side-by-side visual reference of their external appearance prior to 4D analysis.

5.2. Tomato Results

Table 8. Measured parameters and final grades for all tomato samples.

Sample	Defective?	${\mathit{d}}_{\mathbf{Spec}}$	${\mathit{L}}_{\mathit{b}}$ (mm)	a / b / c (mm)	$\mathbf{\Phi }$ (%)	Size	Final Grade
Tomato 1 (no defect)	No	—	—	57.00 / 56.83 / 46.76	93.52	Small	Grade 1 Small
Tomato 2 (defective)	Yes	0.042	9.8	67.50 / 66.34 / 63.14	97.24	Large	Grade 2 Large

summarizes the key 4D parameters and final grades for our two tomato samples. Tomato 1 fell below the 2% spectral-difference threshold and thus followed the Non-Defective branch, while Tomato 2 exceeded the threshold and was routed to the Defective branch.

As shown in Table 8, Tomato 1 registered no spectral defect and was graded by its sphericity alone (“Grade 1”) and its longest span $a = 57.00$ mm placed it in the Small size class. Tomato 2 exceeded the 2% spectral-difference threshold ($d_{\mathrm{Spec}} = 0.042$) and exhibited a bruise length of 9.8 mm, routing it to the Defective branch. Combining its sphericity (97.24%) and bruise-severity band produces a “Grade 2” quality, and its longest span $a = 67.50$ mm yields the Large size class, giving the final label “Grade 2 Large.”

Figure 10 shows a combined RGB image of the two tomatoes discussed in Table 8, providing a side-by-side visual reference of their external appearance prior to 4D analysis.

6. Discussion

Our results demonstrate that fusing hyperspectral and 3D geometry into a single 4D-grading pipeline yields a more complete, objective picture of fruit quality than either modality alone. By flagging subsurface bruising or internal damage via a spectral-difference rule and then quantifying true 3D size and roundness, we can assign USDA-style grades with greater confidence, reduce false negatives on early defects, and minimize the over-grading of misshapen but healthy fruit. In a commercial packing line, this could translate to less manual labor and re-sorting, lower waste rates, and more consistent compliance with buyer contracts. Moreover, because all of our spectral and geometric features reduce to a handful of easily interpretable scalars, the system lends itself to real-time hardware implementation (e.g., GPU pipelines) and straightforward integration into existing conveyor-belt sorters.

The apple results (Table 7) showed that Apple 3, with a spectral-difference score of 3.5% and bruise length of 12.4 mm, was correctly flagged as defective, illustrating the ability of the hyperspectral threshold to capture internal bruising. Apple 2, which was non-defective but had the lowest sphericity (83.4%), demonstrates how shape irregularities alone can reduce grade under the sphericity-based rules. In tomatoes (Table 8), Tomato 2’s high sphericity (97.2%) but defective grade highlights how internal damage cannot be inferred from geometry alone, reinforcing the importance of combining modalities. Furthermore, the measured sphericity ranges (83–97%) are consistent with those reported in previous studies for apple and tomato cultivars, as already discussed in Section 4, supporting the accuracy of the 3D-reconstruction component of our pipeline.

However, a major limitation of this study is the very small sample size, which prevents any statistically robust conclusions about system performance in real-world, highly variable agricultural environments. The results presented here should therefore be interpreted as a proof of concept demonstrating feasibility only. Although the precision of structured-light 3D scanning could theoretically influence geometric parameters such as sphericity and bruise length, the FPP system used in this study has sub-millimeter accuracy, which is sufficient for the size range and defect characteristics of the tested fruits. Additionally, the grading thresholds we employed incorporate margins that minimize the impact of small variations in 3D measurements. Achieving true industrial throughput will require significantly larger and more diverse datasets, as well as more extensive feature registration, to fully optimize the algorithms and improve generalizability across cultivars, defect types, and production conditions.

At the same time, we recognize that real-time deployment will require further optimization. First, computational load could be reduced through adaptive sampling strategies and the use of GPU-based parallel computation to accelerate both hyperspectral and 3D processing [38]. Second, prior studies have demonstrated that robust registration between hyperspectral and 3D data in prior work [25,39]; defects identified directly from hyperspectral analysis could be automatically mapped onto the 3D mesh, eliminating the need for manual 3D-feature extraction and further streamlining the pipeline. Benchmarking the resulting end-to-end pipeline on data transfer rates, per-fruit processing time, and overall computational bottlenecks will require more research and bigger datasets.

Although we did not perform direct quantitative comparisons against single-modality HSI, 3D imaging, or advanced deep-learning approaches, our interpretable decision-tree framework offers a distinct advantage: it provides clear grading logic tied to measurable physical thresholds. This transparency enables stakeholders to understand and adjust thresholds for different cultivars, defect severities, or market requirements without retraining a complex black-box model. This flexibility makes the framework well-suited for early-stage deployment and future adaptation across different packing-line environments. While interpretability is a key strength of our decision-tree framework, it may also limit its ability to capture subtle defects or complex patterns. Future work could explore hybrid approaches that combine the transparency of decision trees with the predictive power of advanced machine learning models.

While we demonstrated 4D grading on bruising in apples and tomatoes, the same framework is readily customizable to any surface or subsurface defect—sunscald, bacterial spot, catface deformities, internal decay, etc.—simply by adjusting the spectral and size thresholds to match each USDA defect definition. In our study, we selected a fixed spectral-difference threshold ($d_{\mathrm{Spec}} \ge 0.02$) based on values reported in the prior literature rather than training a data-driven classifier. This approach reflects both the limited sample size and our emphasis on interpretability, ensuring the grading logic remains transparent and reproducible. In contrast to traditional methods that rely on machine learning (e.g., SVM and ANN) or deep learning to learn decision boundaries from large labeled datasets, our fixed-threshold rule offers a robust, low-complexity alternative appropriate for early-stage deployment. Overall, this proof-of-concept study highlights the potential of 4D hyperspectral/geometry fusion for fruit inspection and its suitability for broader automated quality control applications.

7. Conclusions

In this work, we have proposed a practical, decision-tree-based framework that fuses VNIR/SWIR hyperspectral data with 3D geometric measurements to grade nearly spherical fruits. By first computing Mohsenin’s sphericity index and then applying a simple 2% spectral-difference defect flag, our pipeline routes each specimen into “Defective” or “Non-Defective” branches, uses 3D-bruise-length measurements where appropriate, and finally assigns USDA-style quality and size grades. Applied to a handful of apple and tomato samples, this 4D fusion approach offers an interpretable alternative to single-modality or black-box models, allowing packers to adjust grading thresholds easily for different fruit varieties and market requirements.

While our initial results demonstrate the feasibility of integrating spectral and geometric cues in a unified grading system, further work is needed to automate 3D-parameter extraction, validate performance across larger and more varied datasets, and extend the method to other types of produce. The modular decision-tree structure ensures that, by tuning only a few numerical cutoffs, the same grading logic can be adapted to new fruits or evolving industry standards. We therefore view this 4D hyperspectral approach not as a radical departure but as a flexible, easy-to-integrate alternative that complements existing packing-line technologies and may help improve consistency and objectivity in automated fruit grading.