Flower: Biological, Visual & Computational Insights

• Flower is a multi-faceted subject encompassing botanical development, fine-grained visual classification, robotic manipulation, and advanced computational modeling.
• It serves as a canonical model in gene regulatory networks and spatial diffusion studies while driving innovations in image segmentation and ensemble deep learning for species recognition.
• Recent applications span robotic pollination, intra-floral volatile transport, and federated learning frameworks, highlighting the interdisciplinary significance and practical impacts of flower research.

Searching arXiv for relevant papers on “flower” across biology, computer vision, robotics, and the “Flower” FL framework. In the research literature considered here, a flower is treated simultaneously as a biological structure of angiosperms, as a visually complex object for fine-grained recognition, as a manipulation target in robotic pollination, and as a namesake for several computational systems and algorithms. Across these domains, the term links developmental organization, inter-organ signaling, species identification, perception-driven control, and a set of acronymic methods in machine learning and inverse problems (Poza et al., 2018, Boachon et al., 2024, Gurnani et al., 2017, Beutel et al., 2020).

1. Flower as a developmental and spatially organized biological structure

In Arabidopsis thaliana, the mature flower is organized into four concentric whorls, from outside to inside: sepals, petals, stamens, and carpels. The cited developmental model treats floral patterning as a problem of cell fate determination driven by a gene regulatory network and interprets this process through Waddington’s epigenetic landscape embedded in a reaction–diffusion system (Poza et al., 2018). Within the ABC model used there, A genes are active in the outer two whorls, B genes in the second and third, and C genes in the third and fourth, with organ identity specified by the combinations A alone, A + B, B + C, and C alone.

The same work uses a Boolean gene regulatory network with 13 nodes and reports convergence from all $2^{13}$ initial conditions to 10 attractors, of which the floral-organ attractors are characterized by basin counts

$$c_S=152,\quad c_P=160,\quad c_T=3744,\quad c_C=3608.$$

These counts parameterize a continuous potential

$$F(u,v)=\min\left\{ a_S[(u-u_S)^2+(v-v_S)^2],\, a_P[(u-u_P)^2+(v-v_P)^2],\, a_T[(u-u_T)^2+(v-v_T)^2],\, a_C[(u-u_C)^2+(v-v_C)^2] \right\},$$

with $a_S=1/c_S$, $a_P=1/c_P$, $a_T=1/c_T$, and $a_C=1/c_C$, and basin centers obtained by singular value decomposition. The resulting reaction–diffusion system,

$$\frac{\partial u}{\partial t}=d_1\Delta u+f(u,v),\qquad \frac{\partial v}{\partial t}=d_2\Delta v+g(u,v),$$

with $(f,g)=-\nabla F$, is solved on an annular domain that reflects the radial organization of the floral meristem. The model recovers the wild-type sequence

$$\text{sepals} \rightarrow \text{petals} \rightarrow \text{stamens} \rightarrow \text{carpels},$$

and also reproduces the altered spatial distributions of homeotic mutants such as AP1, Pi, and Ag (Poza et al., 2018).

This formulation makes the flower a canonical genotype–phenotype system in which discrete attractor structure, low-dimensional landscape geometry, and spatial diffusion are explicitly coupled. A plausible implication is that the flower is used here not merely as a developmental example, but as a mathematically tractable system for connecting gene regulation to spatial morphology.

2. Inter-organ volatile transport and reproductive coordination

Recent work on petunia demonstrates that floral volatile organic compounds are not only emitted to the external environment, but can also mediate direct communication between organs within the same flower. The process is termed natural fumigation and is defined as the release of VOCs into the confined internal airspace of a flower bud, followed by absorption of those VOCs by another organ in the same bud (Boachon et al., 2024).

The central molecular component is PhTPS1, a tube-specific sesquiterpene synthase expressed before anthesis in the upper part of the floral tube. When expressed in yeast, PhTPS1 produces a multi-product sesquiterpene blend, mainly germacrene D, bicyclogermacrene, β-cadinene, and germacrene D-4-ol. The relevant biosynthetic relation is summarized as

$$c_S=152,\quad c_P=160,\quad c_T=3744,\quad c_C=3608.$$0

The study distinguishes this tube-derived chemistry from pistil-local production: PhTPS3 and PhTPS4 explain the pistil’s own β-cadinene, whereas PhTPS1 explains the presence in pistils of germacrene D, bicyclogermacrene, and germacrene D-4-ol (Boachon et al., 2024).

Evidence for transport is established through spatial expression analysis, tube removal, stable isotope feeding with $$c_S=152,\quad c_P=160,\quad c_T=3744,\quad c_C=3608.$$1-mevalonolactone, PhTPS1 RNAi knockdown, and gas-phase complementation. In transgenic plants with 92–94% reduced PhTPS1 transcript levels, both tube emission and pistil accumulation of PhTPS1 products fell dramatically; when RNAi pistils were placed inside wild-type tubes for 24 h, the missing sesquiterpenes re-accumulated in the pistils (Boachon et al., 2024). The stigma appears to be a preferential sink, and the study proposes that higher cuticular wax content enhances adsorption or partitioning of lipophilic VOCs.

The reported functions extend beyond scent. Natural fumigation is associated with defense of reproductive tissues, because PhTPS1-RNAi flowers showed increased abundance of a Pseudomonas OTU on the stigma; with regulation of pistil development, because RNAi pistils were lighter and had smaller stigmas and reduced style dimensions; and with reproductive output, because PhTPS1 downregulation reduced seed number by up to 33% (Boachon et al., 2024). The authors further propose that tube-derived sesquiterpenes may act as hormone-like developmental cues coordinating pistil maturation with petal development and floral opening. This suggests that, in at least one system, a flower is an internally communicating volatile microenvironment rather than only an external pollinator signal source.

3. Flowers as objects of image recognition and fine-grained classification

Automated flower classification is presented as a difficult computer-vision problem because species often differ subtly in color, texture, petal arrangement, and shape, while natural images contain clutter, occlusion, and large intra-class variation. One 2017 study uses the Oxford VGG 102-category flower dataset, containing 8,189 images across 102 classes, and adopts a two-stage pipeline: background-removing image segmentation followed by CNN classification (Gurnani et al., 2017). The segmentation stage iteratively removes the most frequent hue values in the background, producing a segmented image with a black background and the flower as the main subject. The classification stage compares fine-tuned AlexNet and GoogLeNet, both initialized from ImageNet/ILSVRC weights and trained with stochastic gradient descent, base learning rate $$c_S=152,\quad c_P=160,\quad c_T=3744,\quad c_C=3608.$$2, linear learning-rate decay, 100 epochs, dropout ratio $$c_S=152,\quad c_P=160,\quad c_T=3744,\quad c_C=3608.$$3, and a softmax output layer

$$c_S=152,\quad c_P=160,\quad c_T=3744,\quad c_C=3608.$$4

GoogLeNet reaches 47.15% top-1 accuracy and 69.17% top-5 accuracy, compared with AlexNet at 43.39% top-1 and 68.68% top-5, against a random top-1 baseline of 0.98% (Gurnani et al., 2017).

A later mobile-oriented study shifts to a 16-class setting using an open-source Kaggle Flowers dataset of 15,742 RGB images split into 80% training, 10% validation, and 10% test. It compares MobileNet, DenseNet121, and Xception, using only the convolutional base of each network, followed by Global Average Pooling and a dense output layer with 16 units and softmax activation (Yurdakul et al., 22 Jan 2026). Images are resized to $$c_S=152,\quad c_P=160,\quad c_T=3744,\quad c_C=3608.$$5 for MobileNet and DenseNet121, and to $$c_S=152,\quad c_P=160,\quad c_T=3744,\quad c_C=3608.$$6 for Xception; online augmentation uses rotation 0.4, width shift 0.2, height shift 0.3, shear 0.2, and zoom 0.2. The reported evaluation metrics include

$$c_S=152,\quad c_P=160,\quad c_T=3744,\quad c_C=3608.$$7

$$c_S=152,\quad c_P=160,\quad c_T=3744,\quad c_C=3608.$$8

and

$$c_S=152,\quad c_P=160,\quad c_T=3744,\quad c_C=3608.$$9

The best model is DenseNet121 with SGD and 0% freezing, achieving 95.84% accuracy, 96.00% precision, 96.00% recall, and 96.00% F1-score (Yurdakul et al., 22 Jan 2026).

Ensemble learning appears in "DeepFlorist" (Khadangi, 2023), developed for the Google Flower Classification using TPUs competition with 16,465 training images, 3,712 validation images, 7,382 test images, and 104 flower species. The system trains DenseNet201, EfficientNet-B4, EfficientNet-B5, and EfficientNet-B6 as base deep classifiers, freezes them, concatenates their outputs or features, and trains a final dense meta-classifier. It uses categorical focal loss,

$$F(u,v)=\min\left\{ a_S[(u-u_S)^2+(v-v_S)^2],\, a_P[(u-u_P)^2+(v-v_P)^2],\, a_T[(u-u_T)^2+(v-v_T)^2],\, a_C[(u-u_C)^2+(v-v_C)^2] \right\},$$0

with Google TPU GRPC, TensorFlow Mirrored Strategy across 8 replicas, batch size 128, Adam, and a learning-rate schedule with exponential decay, ramp-up, and sustain. The method reports 4th place among more than 800 teams and Macro F1-score $$F(u,v)=\min\left\{ a_S[(u-u_S)^2+(v-v_S)^2],\, a_P[(u-u_P)^2+(v-v_P)^2],\, a_T[(u-u_T)^2+(v-v_T)^2],\, a_C[(u-u_C)^2+(v-v_C)^2] \right\},$$1 on the test set, with the meta-classifier outperforming all individual base classifiers (Khadangi, 2023).

Before end-to-end deep learning became dominant in this literature, orchid identification was studied through content-based flower image retrieval. The orchid-specific system uses MSRM segmentation, extracts shape and HSV color features from both the whole flower and the lip (labellum), and classifies with multi-class SVM using LIBSVM (Apriyanti et al., 2014). The main reported gain is that using both flower and lip improves validation accuracy to 85.33% and testing accuracy to 79.33%, about $$F(u,v)=\min\left\{ a_S[(u-u_S)^2+(v-v_S)^2],\, a_P[(u-u_P)^2+(v-v_P)^2],\, a_T[(u-u_T)^2+(v-v_T)^2],\, a_C[(u-u_C)^2+(v-v_C)^2] \right\},$$2 higher than using only flower features. The most dominant features are Centroid Contour Distance, Moment Invariant, and HSV Color (Apriyanti et al., 2014).

At orchard scale, flowers are treated as segmentation targets for bloom-intensity estimation. DeepLab+RGR is trained on apple flowers and applied without dataset-specific retraining to apple, peach, and pear images, using DeepLab-ResNet semantic segmentation followed by region growing refinement (Dias et al., 2018). On AppleA, the method reports IoU 71.4%, $$F(u,v)=\min\left\{ a_S[(u-u_S)^2+(v-v_S)^2],\, a_P[(u-u_P)^2+(v-v_P)^2],\, a_T[(u-u_T)^2+(v-v_T)^2],\, a_C[(u-u_C)^2+(v-v_C)^2] \right\},$$3 83.3%, recall 87.7%, and precision 79.4%; on Pear, IoU 75.4%, $$F(u,v)=\min\left\{ a_S[(u-u_S)^2+(v-v_S)^2],\, a_P[(u-u_P)^2+(v-v_P)^2],\, a_T[(u-u_T)^2+(v-v_T)^2],\, a_C[(u-u_C)^2+(v-v_C)^2] \right\},$$4 86.0%, recall 79.2%, and precision 94.1% (Dias et al., 2018). This suggests that in computer vision the flower is both a fine-grained taxonomic object and an agricultural counting primitive.

4. Flowers as robotic perception and manipulation targets

Robotic pollination research treats the flower as a small, fragile, pose-sensitive contact target. In the BrambleBee system, the Flower Interaction Subsystem performs a complete perception-to-contact pipeline for individual small bramble flowers: workspace mapping, flower detection and pose estimation, trajectory planning, visual servoing, and contact pollination with a custom end-effector (Strader et al., 2019). Detection uses a two-stage pipeline of naive Bayes pixel segmentation and transfer learning with Inception-v3. The segmentation stage applies

$$F(u,v)=\min\left\{ a_S[(u-u_S)^2+(v-v_S)^2],\, a_P[(u-u_P)^2+(v-v_P)^2],\, a_T[(u-u_T)^2+(v-v_T)^2],\, a_C[(u-u_C)^2+(v-v_C)^2] \right\},$$5

while CNN refinement uses softmax

$$F(u,v)=\min\left\{ a_S[(u-u_S)^2+(v-v_S)^2],\, a_P[(u-u_P)^2+(v-v_P)^2],\, a_T[(u-u_T)^2+(v-v_T)^2],\, a_C[(u-u_C)^2+(v-v_C)^2] \right\},$$6

and cross-entropy

$$F(u,v)=\min\left\{ a_S[(u-u_S)^2+(v-v_S)^2],\, a_P[(u-u_P)^2+(v-v_P)^2],\, a_T[(u-u_T)^2+(v-v_T)^2],\, a_C[(u-u_C)^2+(v-v_C)^2] \right\},$$7

The system reports 93.1% detection accuracy and a 76.9% pollination success rate on high-fidelity artificial bramble flowers (Strader et al., 2019).

Pose-sensitive pollination remains a central bottleneck. FloPE addresses 6-DoF flower pose estimation for computationally constrained robotic pollination using 3D Gaussian Splatting, teacher–student knowledge distillation, direct pose regression, and Extended Kalman Filter refinement (Shrestha et al., 8 Mar 2025). The synthetic scene representation uses Gaussian primitives

$$F(u,v)=\min\left\{ a_S[(u-u_S)^2+(v-v_S)^2],\, a_P[(u-u_P)^2+(v-v_P)^2],\, a_T[(u-u_T)^2+(v-v_T)^2],\, a_C[(u-u_C)^2+(v-v_C)^2] \right\},$$8

rendered as

$$F(u,v)=\min\left\{ a_S[(u-u_S)^2+(v-v_S)^2],\, a_P[(u-u_P)^2+(v-v_P)^2],\, a_T[(u-u_T)^2+(v-v_T)^2],\, a_C[(u-u_C)^2+(v-v_C)^2] \right\},$$9

Flower pose is represented as $a_S=1/c_S$0; orientation is regressed in $a_S=1/c_S$1 and projected to $a_S=1/c_S$2 via SVD, with loss $a_S=1/c_S$3. Position is lifted from depth by

$a_S=1/c_S$4

After refinement, FloPE reports translational error 0.6 cm, rotational error 19.14°, and pose success 77.78%, while maintaining 15.5 FPS on an RTX 3090 Ti and 3.45 FPS on Jetson; pollination success reaches 61.36% on Stickbug and 78.75% on UR5 (Shrestha et al., 8 Mar 2025).

A complementary 3D approach for strawberry flowers reconstructs plant point clouds with a FarmBot-based platform and estimates flower pose from six orthographic-like occupancy-grid projections (Muriki et al., 2 Sep 2025). Flowers are detected in 2D with YOLOv10 or Roboflow 3.0 Object Detection, back-projected to 3D, clustered with DBSCAN using $a_S=1/c_S$5 and $a_S=1/c_S$6, and fit with superellipsoid, paraboloid, or plane models. The plane model performs best, with mean angular error 7.7° and median error 5.9°, while approximately 80.3% of flowers are detected across seven FarmBot scans (Muriki et al., 2 Sep 2025).

In vertical farming, contactless pollination motivates an aerial manipulator that detects, localizes, and approaches flowers without touching them. The proposed UAV platform integrates RGB-D flower detection, YOLO-based real-time localization, Model Predictive Path Integral control, PX4, and a lightweight 2-DoF manipulator (Jin et al., 7 May 2026). The quadrotor model is written as

$a_S=1/c_S$7

while the combined system uses

$a_S=1/c_S$8

The desired UAV standoff position is

$a_S=1/c_S$9

with a real-world standoff on the order of $a_P=1/c_P$0 cm. The platform is validated in MuJoCo and in a $a_P=1/c_P$1 m indoor laboratory, with successful alignment defined as end-effector distance error within 5 cm (Jin et al., 7 May 2026).

Taken together, these systems treat the flower not as a generic object but as a target whose geometry, fragility, and reproductive anatomy impose unusually strict constraints on detection, localization, orientation inference, and final approach.

5. Flowers as physical shapes, field perturbations, and patterns

Flowers also appear as objects in physical sensing problems. BeeNet reconstructs flower shapes from electric fields generated when a positively charged bee approaches a polarisable flower (Turley et al., 15 Aug 2025). The flower is modeled in two dimensions as a dielectric region with interior $a_P=1/c_P$2, exterior $a_P=1/c_P$3, boundary $a_P=1/c_P$4, and electric potential satisfying

$a_P=1/c_P$5

with continuity and permittivity-weighted flux conditions across $a_P=1/c_P$6. Training data are generated numerically using the two-domain AAA-least squares method, and the network input is based on perturbation quantities

$a_P=1/c_P$7

evaluated on an $a_P=1/c_P$8 grid and downsampled to $a_P=1/c_P$9. BeeNet uses a ResNet101-based Dynamic U-Net with 318,616,725 parameters and 121 layers, trained on 1,979 simulated examples. It achieves mean F1 score 0.912 on the validation set and 0.842 on unseen four-petal flowers, with performance peaking at a bee distance of 8 petal radii where mean F1 reaches 0.927 (Turley et al., 15 Aug 2025). This indicates that flower geometry can be inferred from field perturbations alone.

The word “flower” also labels a pattern rather than an organism in soft-matter physics. An evaporating sessile droplet containing 1% w/w PEG in M2B buffer forms a regular, radially aligned flower-like deposition pattern with three regions: an outer ring, an intermediate region with petals, and a central region with anisotropic compact deposition (Nasirimarekani, 2024). The petals have wavelength about 30–70 μm and average length about 120 μm for a droplet of radius $a_T=1/c_T$0 μm. The proposed mechanism is

$a_T=1/c_T$1

The study attributes the morphology to salting-out-induced PEG phase separation, an entropic outward transport termed phase separation bursting flow, and symmetry breaking during contact-line contraction (Nasirimarekani, 2024).

These examples broaden the technical meaning of flower. In one case it is a dielectric shape inferred from electrostatic perturbation; in the other it is a deposition morphology generated by nonequilibrium transport. A plausible implication is that floral form functions here as a geometric prior even when the underlying question is not botanical.

6. “Flower” and “FLOWER” as names in machine learning systems

Separate from biological usage, “Flower” is also the name of an open-source federated learning framework. "Flower: A Friendly Federated Learning Research Framework" describes Flower as an end-to-end FL framework designed to make federated learning research more scalable and more realistic, with explicit design goals of being scalable, client-agnostic, communication-agnostic, privacy-agnostic, and flexible (Beutel et al., 2020). Its server-side architecture centers on ClientManager, the FL loop, and Strategy; communication uses bi-directional gRPC streams and raw byte-array messages; the Virtual Client Engine builds on Ray to support large-scale simulation; and the Edge Client Engine supports Raspberry Pi, NVIDIA Jetson devices, and Android smartphones. The paper reports experiments with up to 15 million clients using two NVIDIA V100 GPUs and a 22-core Intel Xeon CPU, and lists built-in strategies including FedAvg, Fault Tolerant FedAvg, FedProx, QFedAvg, and FedOptim variants such as FedAdagrad, FedYogi, and FedAdam (Beutel et al., 2020).

A later interoperability paper places Flower in a broader FL stack alongside NVIDIA FLARE (Roth et al., 2024). There, Flower is described as dedicated to implementing a cohesive approach to FL, analytics, and evaluation, while FLARE is presented as an enterprise-ready, resilient runtime for production environments. The integration routes Flower’s gRPC messages through FLARE so that Flower applications can run in the FLARE runtime without modification, using components such as Flower SuperLink and SuperNodes on the Flower side and local gRPC servers or clients within FLARE (Roth et al., 2024).

The name also recurs in acronymic methods unrelated to botany or federated learning. "FLOWER: Flow-Based Estimated Gaussian Guidance for General Speech Restoration" introduces a conditioning strategy in which a conditional normalizing flow maps clean speech to a Gaussian prior,

$a_T=1/c_T$2

and injects the resulting guidance into a diffusion or flow-matching generator (Yang et al., 3 May 2025). The total objective is

$a_T=1/c_T$3

"Flower" in recommender systems refers to the Flow-guided fine-tuning recommender, which replaces plain supervised fine-tuning with a GFlowNet-based process-supervision signal over item-title prefix trees (Gao et al., 10 Mar 2025). Its core objective combines

$a_T=1/c_T$4

and defines token-level process reward by

$a_T=1/c_T$5

Finally, "FLOWER: A Flow-Matching Solver for Inverse Problems" denotes a posterior-aware inverse solver that iterates flow-consistent destination estimation, proximal measurement refinement, and time progression (Pourya et al., 30 Sep 2025). Its destination estimate is

$a_T=1/c_T$6

followed by a proximal update toward data consistency (Pourya et al., 30 Sep 2025).

These acronymic uses are semantically independent of the biological flower. Their coexistence in recent literature illustrates that “Flower” functions both as an object of study and as a durable naming convention for frameworks and methods across federated learning, speech restoration, recommendation, and inverse problems.