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Hieu D. Nguyen

Publications and source records attributed to Hieu D. Nguyen.

At least 19 recordsLinked to original sources

Combining Object Detection with Geometry-Aware Clustering to Distinguish Overlapping Plants in UAV Imagery

Reliable plant-level information from unmanned aerial vehicle (UAV) imagery is important for automated crop monitoring. However, in dense crop canopies, adjacent plants frequently overlap and are detected as a single object, reducing the reliability of plant-level measurements. This study presents a geometry-aware post-detection framework for resolving overlapping plant instances using standard RGB UAV imagery. The framework combines object detection with geometric clustering of plant components. Leaves or branches detected within each bush-level region are represented using two complementary geometric features: component centroids and radial intersection points (RIPs) derived from detected plant structures. K-means and Gaussian mixture models determine whether a detected region contains a single plant or two overlapping plants. Density filtering suppresses spurious radial intersections, and a post-pipeline ensemble combines spatial and directional geometric information. The framework was evaluated using UAV imagery of eggplant and tomato crops under field conditions. Centroid-based clustering achieved an F1-score of 0.89 for eggplant, while the combined centroid-RIP approach achieved the best tomato performance, with an accuracy of 0.80, precision of 1.00, and F1-score of 0.75 using K-means. Density filtering substantially improved RIP-based clustering for tomato. The proposed approach provides a lightweight, modular engineering solution that can be integrated with existing RGB UAV monitoring pipelines without additional depth sensors, pixel-level segmentation, three-dimensional reconstruction, or retraining of the primary bush detector. The results demonstrate that geometric reasoning applied to existing detector outputs can complement deep-learning-based object detection and improve plant-level interpretation in dense agricultural canopies.

cs.CV

Accurate Crop Yield Estimation of Blueberries using Deep Learning and Smart Drones

We present an AI pipeline that involves using smart drones equipped with computer vision to obtain a more accurate fruit count and yield estimation of the number of blueberries in a field. The core components are two object-detection models based on the YOLO deep learning architecture: a Bush Model that is able to detect blueberry bushes from images captured at low altitudes and at different angles, and a Berry Model that can detect individual berries that are visible on a bush. Together, both models allow for more accurate crop yield estimation by allowing intelligent control of the drone's position and camera to safely capture side-view images of bushes up close. In addition to providing experimental results for our models, which show good accuracy in terms of precision and recall when captured images are cropped around the foreground center bush, we also describe how to deploy our models to map out blueberry fields using different sampling strategies, and discuss the challenges of annotating very small objects (blueberries) and difficulties in evaluating the effectiveness of our models.

cs.CV

Optimal N-ary ECOC Matrices for Ensemble Classification

A new recursive construction of $N$-ary error-correcting output code (ECOC) matrices for ensemble classification methods is presented, generalizing the classic doubling construction for binary Hadamard matrices. Given any prime integer $N$, this deterministic construction generates base-$N$ symmetric square matrices $M$ of prime-power dimension having optimal minimum Hamming distance between any two of its rows and columns. Experimental results for six datasets demonstrate that using these deterministic coding matrices for $N$-ary ECOC classification yields comparable and in many cases higher accuracy compared to using randomly generated coding matrices. This is particular true when $N$ is adaptively chosen so that the dimension of $M$ matches closely with the number of classes in a dataset, which reduces the loss in minimum Hamming distance when $M$ is truncated to fit the dataset. This is verified through a distance formula for $M$ which shows that these adaptive matrices have significantly higher minimum Hamming distance in comparison to randomly generated ones.

cs.LG

Ensemble Learning using Error Correcting Output Codes: New Classification Error Bounds

New bounds on classification error rates for the error-correcting output code (ECOC) approach in machine learning are presented. These bounds have exponential decay complexity with respect to codeword length and theoretically validate the effectiveness of the ECOC approach. Bounds are derived for two different models: the first under the assumption that all base classifiers are independent and the second under the assumption that all base classifiers are mutually correlated up to first-order. Moreover, we perform ECOC classification on six datasets and compare their error rates with our bounds to experimentally validate our work and show the effect of correlation on classification accuracy.

cs.LG

The area of the Mandelbrot set and Zagier's conjecture

We prove Zagier's conjecture regarding the 2-adic valuation of the coefficients $\{b_m\}$ that appear in Ewing and Schober's series formula for the area of the Mandelbrot set in the case where $m\equiv 2 \mod 4$.

math.NT

Partitions of Equiangular Tight Frames

We present a new efficient algorithm to construct partitions of a special class of equiangular tight frames (ETFs) that satisfy the operator norm bound established by a theorem of Marcus, Spielman, and Srivastava (MSS), which they proved as a corollary yields a positive solution to the Kadison-Singer problem. In particular, we prove that certain diagonal partitions of complex ETFs generated by recursive skew-symmetric conference matrices yield a refinement of the MSS bound. Moreover, we prove that all partitions of ETFs whose largest subset has cardinality three or less also satisfy the MSS bound.

math.FA

New Approximations for the Area of the Mandelbrot Set

Due to its fractal nature, much about the area of the Mandelbrot set $M$ remains to be understood. While a series formula has been derived by Ewing and Schober to calculate the area of $M$ by considering its complement inside the Riemann sphere, to date the exact value of this area remains unknown. This paper presents new improved upper bounds for the area based on a parallel computing algorithm and for the 2-adic valuation of the series coefficients in terms of the sum-of-digits function.

math.DS

A Digital Binomial Theorem for Sheffer Sequences

We extend the digital binomial theorem to Sheffer polynomial sequences by demonstrating that their corresponding Sierpiński matrices satisfy a multiplication property that is equivalent to the convolution identity for Sheffer sequences.

math.NT

A $q$-Digital Binomial Theorem

We present a multivariable generalization of the digital binomial theorem from which a q-analog is derived as a special case.

math.NT

Group Symmetries of Complementary Code Matrices

We characterize group symmetries of poly-phase complementary code matrices (CCMs), which we use to classify CCMs in terms of their equivalence classes. We also present classification results for CCMs of dimension $N\times 4$ where $N=2,3,4,5,6$. Finally, we present a new construction to generate quad-phase CCMs from ternary CCMs and compare this to other existing constructions that focus on generating CCMs from those of smaller dimensions.

cs.IT

A Generalization of the Digital Binomial Theorem

We prove a generalization of the digital binomial theorem by constructing a one-parameter subgroup of generalized Sierpinski matrices. In addition, we derive new formulas for the coefficients of Prouhet-Thue-Morse polynomials and describe group relations satisfied by generating matrices defined in terms of these Sierpinski matrices.

math.NT

A Digital Binomial Theorem

We present a triangle of connections between the Sierpinski triangle, the sum-of-digits function, and the Binomial Theorem via a one-parameter family of Sierpinski matrices, which encodes a digital version of the Binomial Theorem.

math.NT

A New Proof of the Prouhet-Tarry-Escott Problem

The famous Prouhet-Tarry-Escott problem seeks collections of mutually disjoint sets of non-negative integers having equal sums of like powers. In this paper we present a new proof of the solution to this problem by deriving a generalization of the product generating function formula for the classical Prouhet-Thue-Morse sequence.

math.NT

Doppler Tolerance, Complementary Code Sets and the Generalized Thue-Morse Sequence

We generalize the construction of Doppler-tolerant Golay complementary waveforms by Pezeshki-Calderbank-Moran-Howard to complementary code sets having more than two codes. This is accomplished by exploiting number-theoretic results involving the sum-of-digits function, equal sums of like powers, and a generalization to more than two symbols of the classical two-symbol Prouhet-Thue-Morse sequence.

cs.IT

A Mixing of Prouhet-Thue-Morse Sequences and Rademacher Functions

A novel generalization of the Prouhet-Thue-Morse sequence to binary $\pm 1$-weight sequences is presented. Derived from Rademacher functions, these weight sequences are shown to satisfy interesting orthogonality and recurrence relations. In addition, a result useful in describing these weight sequences as sidelobes of Doppler tolerant waveforms in radar is established.

math.NT