---
title: Perceptual Boundary Sampling in ANNs
url: https://www.emergentmind.com/topics/perceptual-boundary-sampling
type: topic
---

# Perceptual Boundary Sampling in ANNs

Searching arXiv for recent papers on perceptual boundary sampling and closely related formulations.
Perceptual boundary sampling, in the ANN-centered usage documented here, denotes the deliberate selection or synthesis of samples that lie near a model’s decision frontier in a representation space intended to encode perceptual or semantic structure. In contemporary work, that boundary may be defined in a frozen pretrained feature space for active finetuning, or in the output geometry of a classifier coupled to a diffusion prior for synthesizing ambiguous stimuli that elicit variable human judgments [2403.10069], [2505.03641], [2507.14549]. Adjacent literatures use closely related boundary-sample constructions for hardware fingerprinting through imperceptible perturbations [2106.07303], while an earlier image-analysis line treats perceptually significant boundaries as salient level lines selected by a-contrario criteria [1210.3718]. Across these formulations, the unifying operation is to privilege ambiguous or borderline cases rather than only central exemplars, although the operational goal varies substantially.

## 1. Scope and principal formulations

In the literature represented here, perceptual boundary sampling is not a single algorithm but a family of boundary-oriented procedures. The central distinction is between **selection** of existing unlabeled samples near a learned boundary and **generation** of new samples that are driven toward such a boundary. A second distinction concerns what counts as “perceptual”: frozen pretrained features, classifier output probabilities, human response distributions, or salient image contours.

| Setting | Boundary representation | Primary objective |
|---|---|---|
| Bi-Level Active Finetuning | Frozen pretrained features \(f_i=f(x_i;w_0)\in\mathbb R^d\) | One-shot annotation selection combining diversity and uncertainty [2403.10069] |
| BAM / variMNIST | ANN decision boundaries with classifier-guided diffusion | Generate ambiguous digit stimuli, align models to group and individual behavior, and manipulate paired decisions [2505.03641] |
| varEmotion | ANN emotion-class boundaries with two-stage diffusion | Generate ambiguous facial-expression stimuli and align models to human perceptual variability [2507.14549] |
| Related boundary-based work | Microarchitecture-sensitive label flips; salient level lines | Watermarking and perceptual boundary saliency [2106.07303], [1210.3718] |

A plausible implication is that the term now spans both **decision-boundary exploitation** and **boundary-centered stimulus design**. The former uses a pretrained model’s geometry as a proxy for informative uncertainty; the latter treats ANN ambiguity as a generator of stimuli that are likely to induce perceptual divergence in humans.

## 2. Feature-space boundary sampling in bi-level active finetuning

The clearest selection-based formulation appears in the Bi-Level Active Finetuning framework, which defines the goal of boundary sample selection as identifying, within each pseudo-class, those unannotated examples that lie closest to the “decision frontier” separating that class from its neighbors in the pretrained model’s feature space [2403.10069]. Ground-truth labels are unavailable at selection time, so the procedure operates entirely on the geometry of frozen features \(f_i=f(x_i;w_0)\in\mathbb R^d\).

The framework is explicitly two-stage. First, it performs core sample selection for diversity. It chooses \(K\) pseudo-class centers via a diversity-oriented method such as ActiveFT or K-Means; in practice it uses ActiveFT, which solves
\[
\theta^*=\arg\min_\theta D(p_{f_u},p_\theta)-\lambda\cdot R(\theta)
\]
under \(\|\theta^j\|_2=1\) for \(j=1\ldots K\), and then picks, for each \(\theta^j\), the nearest feature
\[
f_{s_j}=\arg\max_{f_k\in F^u}\mathrm{sim}(f_k,\theta^j).
\]
These \(K\) samples become the initial centers. Every unlabeled feature is then assigned to the nearest center by Euclidean distance, partitioning the pool into pseudo-classes.

The second stage performs boundary sampling for uncertainty. Because the boundary stage is highly sensitive to outliers, BiLAF first applies an unsupervised denoising method termed Iterative Density-based Clustering. For a point \(x_j\) with feature \(f_j\), its density distance is defined as the average distance to its \(k\) nearest neighbors within the currently growing cluster:
\[
\rho(f_j)=\frac{1}{k}\sum_{l=1}^k D(f_j,f_{n_{j,l}}).
\]
Starting from \(U_i\leftarrow\{c_i\}\), the cluster grows by repeatedly adding the \(\lfloor P_{\rm in}\cdot |U_i^0|\rfloor\) points with smallest \(\rho\). After the cluster reaches the full candidate set, the last \(P_{\rm rm}\cdot |U_i|\) points added are pruned as noise.

Boundary proximity is then quantified by an intra-class distance
\[
d_{\rm intra}(x_j)=\frac{1}{|U_i|}\sum_{\ell\in U_i}D(f_j,f_\ell),
\]
an inter-class distance to the nearest other center
\[
d_{\rm inter}(x_j)=\min_{c_l:l\neq i}D(f_j,f_{c_l}),
\]
and the Boundary Score
\[
BS(x_j)=\frac{d_{\rm inter}(x_j)-d_{\rm intra}(x_j)}{\max\{d_{\rm inter},d_{\rm intra}\}}.
\]
A small Boundary Score indicates a point close to another class’s prototype yet not overly deep inside its own cluster. To avoid repeatedly sampling the same inter-class seam, the method adds an opponent penalty: if \(t_l\) is the count of already-selected boundary points that were closest to center \(c_l\), future inter-class distances are inflated by \(\delta^{t_l}\), yielding
\[
BS(x_j)=\min_{l\neq i}\frac{\delta^{t_l}\cdot D(f_j,f_{c_l})-d_{\rm intra}(f_j)}{\max\{\delta^{t_l}\cdot D(f_j,f_{c_l}),d_{\rm intra}(f_j)\}}.
\]

Selection is iterative. Each pseudo-class receives a sub-budget
\[
B_i=B\cdot |U_i|/N_{\rm total},
\]
and the algorithm repeatedly picks the point with minimum \(BS\), adds it to the global annotation set, increments the opponent count for the center achieving the minimum, and removes the \(|U_i|/B_i\) nearest neighbors of the selected point to avoid redundancy. The complete procedure is given as Algorithm 1 in the paper [2403.10069].

The implementation is explicitly intended to scale. The reported feature dimension is \(d\approx 384\) for DeiT-Small/DINO, the unlabeled pool reaches \(N\) up to \(1.28\,\mathrm M\) on ImageNet, and \(K\) is typically set to \(0.5\%\) of \(N\). With \(k=10\), \(P_{\rm in}=P_{\rm rm}=0.1\), \(\delta=1.1\), and optimized vectorized kernels, ImageNet-scale pools are processed in a few hours on two RTX 3090 GPUs. Supervised finetuning uses batch size \(256\), SGD with learning rate \(3\times 10^{-3}\), weight decay \(10^{-4}\), momentum \(0.9\), and cosine decay for \(1{,}000\) epochs, except \(300\) epochs for \(5\%\) ImageNet [2403.10069].

The empirical motivation for the method is that diversity alone leaves boundary regions undersampled. Across CIFAR10, CIFAR100, and ImageNet with annotation budgets from \(0.5\%\) to \(10\%\), BiLAF is reported to outperform both purely diversity-based ActiveFT and traditional active learning methods. The paper reports, for example, CIFAR100 at \(1\%\): ActiveFT \(26.1\%\) versus BiLAF \(31.8\%\); at \(2\%\): \(40.7\%\) versus \(43.5\%\); at \(5\%\): \(54.6\%\) versus \(62.8\%\); and ImageNet at \(5\%\): \(65.3\%\) versus \(66.2\%\). Qualitative t-SNE plots are described as showing that core-only methods leave many boundary regions unsampled, whereas BiLAF “pins down support points along each inter-class seam” [2403.10069].

This framework explicitly connects itself to perceptual boundary sampling by “lifting” classical uncertainty sampling into the pretrained model’s “perceptual” feature space, where distances encode semantic relations. Under tight annotation budgets, the stated rationale is that a classifier trained only on central exemplars tends to misplace its boundaries; boundary-targeted annotation forces adjustment precisely where errors are likely to occur [2403.10069].

## 3. Diffusion-guided perceptual boundaries in digit recognition

A generative and human-centered formulation is introduced by BAM, the Boundary Alignment & Manipulation framework, which combines perceptual boundary sampling in ANNs with human behavioral experiments to study perceptual variability [2505.03641]. The setup begins with a pre-trained ANN classifier, or two classifiers for controversial sampling, together with a diffusion model \(p(x_t)\) serving as a natural-image prior.

At each reverse diffusion step, the sample is updated by
\[
x_{t-1}=DDPM^{-}(x_t)-\gamma\nabla_{x_t}\mathcal L_{\rm guide}(x_t),
\]
where \(DDPM^{-}\) is the unconditioned denoising step, \(\gamma\) is a guidance strength, and \(\mathcal L_{\rm guide}\) encourages boundary sampling. Two losses are used. Uncertainty guidance is designed to place a sample near a single model’s decision boundary:
\[
\mathcal L_{\rm u}(x)=H\bigl(p(y\mid x),q_{\rm unif}(y)\bigr),
\quad
q_{\rm unif}(y)=\frac12[\,\![y=i]+\![y=j]\,].
\]
Controversial guidance is designed to maximize disagreement between two models:
\[
\mathcal L_{\rm c}(x)
=
H\bigl(p_1(y\mid x),q_1(y)\bigr)+H\bigl(p_2(y\mid x),q_2(y)\bigr),
\]
with \(q_1\) placing mass on class \(i\) and \(q_2\) on class \(j\). Optionally, a small MSE regularizer toward a reference MNIST digit \(x_{\rm ref}\) can be added:
\[
\mathcal L_{\rm guide}(x)
=
\mathcal L_{\rm u}(x)\ \text{or}\ \mathcal L_{\rm c}(x)
+\alpha\|x-x_{\rm ref}\|_2^2,
\quad \alpha\ll 1.
\]
The framework states that it relies on a classifier-guided diffusion prior, specifically classifier-free guidance, rather than direct pixel-space adversarial perturbations, in order to keep samples in-distribution and avoid heavy noise [2505.03641].

BAM consists of three stages. The first stage is labeling: approximately \(20{,}000\) images are sampled by uncertainty or controversial guidance across all digit pairs \((i,j)\), then shown to many participants in a 10-way digit classification task. For each image, the recorded quantities are the human choice distribution \(h(x)=[h_0,\dots,h_9]\), response time, and entropy \(H(h)\). After sentinel-trial filtering, \(246\) participants remain out of \(400\), yielding \(116{,}715\) valid trials and \(19{,}943\) images in the variMNIST dataset; the same description also states that each participant completed \(500\) trials, for a total of \(123\)k trials [2505.03641].

The second stage is alignment. Starting from a base classifier trained on MNIST, BAM fine-tunes a GroupNet on MNIST \(\cup\) variMNIST in a \(1{:}1\) ratio and then an IndivNet per participant using a mix ratio \(\mathrm{variMNIST}\text{-}i : \mathrm{variMNIST} : \mathrm{MNIST} = 2{:}1{:}1\). The training objective is ordinary cross-entropy on human-labeled 10-way target distributions. The reported effect is that GroupNet and IndivNet retain approximately \(99\%\) accuracy on MNIST, gain approximately \(20\%\) on variMNIST, and that IndivNet adds approximately \(5\%\) on the individual subset variMNIST-i. The quantitative summary given later in the paper states BaseNet accuracy of approximately \(60\%\) on variMNIST, GroupNet approximately \(80\%\), and IndivNet approximately \(85\%\) on variMNIST-i; for a VGG example, the Spearman correlation between model-predicted entropy and human entropy increases from \(0.08\) to \(0.74\) after group fine-tuning [2505.03641].

The third stage is manipulation. For a pair of participants \(A,B\), BAM takes their two IndivNet models \((f_A,f_B)\) and generates new controversial images using
\[
\mathcal L_{\rm c}(x)=H\bigl(p_A(y|x),q_A\bigr)+H\bigl(p_B(y|x),q_B\bigr),
\]
with \(q_A\) pushing toward \(o_1\) and \(q_B\) toward \(o_2\). Approximately \(180\) such stimuli are presented to each pair in lab conditions, and the outcome of interest is whether \(A\) reports \(o_1\) while \(B\) reports \(o_2\). In paired manipulation experiments described as involving \(18\) in-lab participants forming \(18\) pairs, individually generated images improve the “success” rate by approximately \(3\%\) and the directional “targeted ratio” by approximately \(12\%\) over vanilla variMNIST stimuli, with \(p<0.001\) for both [2505.03641].

The behavioral evaluation formalizes three categories for guided class pairs \(o_1,o_2\). A sample is a **success** if \(p(o_1)+p(o_2)\ge 0.8\) and \(\min\{p(o_1),p(o_2)\}\ge 0.1\); **bias** if \(p(o_1)+p(o_2)\ge 0.8\) but \(\min<0.1\); and **failure** otherwise. Across all variMNIST images, success plus bias is approximately \(80\%\), and over half of the images have human-response entropy greater than zero [2505.03641].

The BAM account explicitly argues that decision-boundary regions of ANNs correspond to maximal classifier uncertainty and that prior psychophysics places maximal human perceptual variability near categorical boundaries. On that basis, images synthesized on ANN boundaries are treated as intrinsically likely to induce high human ambiguity [2505.03641].

## 4. Perceptual-boundary sampling for facial-expression variability

A parallel formulation is developed for facial expressions, where the perceptual boundary is defined for a \(C\)-way ANN classifier \(f\) by the locus of inputs \(x\) for which two target emotions \(c_1,c_2\) are balanced, for example when \(z_{c_1}(x)=z_{c_2}(x)\), equivalently \(p_{c_1}(x)=p_{c_2}(x)\) [2507.14549]. Perceptual-boundary sampling is then the generation of new face images near such boundaries, so that the classifier assigns both classes high and roughly equal probability.

The formal construction introduces a target distribution \(q\) over emotions with
\[
q_k=
\begin{cases}
\frac12 & \text{if } k\in\{c_1,c_2\},\\
0 & \text{otherwise},
\end{cases}
\]
and an uncertainty guidance loss
\[
L_{\rm unc}(x)=-\sum_k q_k\cdot \log p_k(x),
\]
which is described as maximized when \(p_{c_1}=p_{c_2}=0.5\) and the other probabilities approach zero. The paper also notes an alternative expression, \(\mathrm{loss}(x,y)=-p(y|x)\cdot q(y)\), interpreted as encouraging high network mass on the two target classes and low mass elsewhere [2507.14549].

Because direct gradient ascent on \(L_{\rm unc}\) is reported to produce noisy and non-photorealistic results, the method embeds the loss in a two-stage diffusion pipeline. In Stage 1, an embedding \(e_T\sim N(0,I)\) is iteratively denoised with uncertainty guidance:
\[
e_{t-1}=DDPM^{-}(e_t)-\gamma\cdot \nabla_{e_t}L_{\rm unc}(x(e_t)),
\]
with the paper reporting \(\gamma=0.5\). In Stage 2, the final guided embedding \(e_0\) is given to Stable Diffusion XL with prompt guidance only, producing a fully rendered RGB face image [2507.14549].

Post-generation filtering is central to the method. Each candidate image is fed back through the ANN, and an image is kept only if both target-class activations exceed class-specific thresholds \(k_c\), where each threshold is set to the \(75\)th percentile of that class’s activation on the RAF-DB real-image distribution:
\[
p_{c_1}(x)>k_{c_1}\quad \text{and}\quad p_{c_2}(x)>k_{c_2}.
\]
The stated purpose is to retain only samples genuinely in the high-uncertainty overlap region of the two emotions [2507.14549].

This procedure is used to construct the varEmotion dataset. For each of the \(15\) unordered emotion pairs from six basic classes, the pipeline produces candidate faces; after filtering, \(1{,}678\) images remain. These are shown in randomized order to \(100\) online participants, of whom \(66\) pass sentinel trials, in a 6-way forced-choice emotion labeling task. Each image is seen by approximately \(13\) participants, for a total of \(22{,}450\) trials. The recorded response for image \(x\) is the empirical human choice distribution
\[
r_h(x)=[n_1,\dots,n_6]/N,
\]
with \(N\approx 13\) [2507.14549].

The evaluation uses both ANN-side and human-side criteria. Human perceptual uncertainty is quantified by entropy
\[
H_h(x)=-\sum_{i=1}^6 p_i^h\log p_i^h.
\]
For guided classes with empirical human fractions \(p_1,p_2\), a sample is categorized as **Success** if \(\min(p_1,p_2)>0.25\) and \(p_1+p_2>0.6\), **Bias** if \(\min(p_1,p_2)<0.25\) and \(p_1+p_2>0.6\), and **Failure** if \(p_1+p_2<0.6\). Roughly \(80\%\) of the images fall into success plus bias, which the paper interprets as effective two-class guidance [2507.14549].

The principal empirical claim is that ANN-confusing facial-expression stimuli also provoke heightened human perceptual uncertainty. The entropy distribution over the \(1{,}678\) images is described as concentrated above zero, indicating that most boundary images induce split judgments. On the modeling side, three architectures—CLIP + MLP, DAN, and ResEmoNet—are fine-tuned with varEmotion mixed with RAF-DB at a \(2{:}1\) ratio under group and individual regimes. Group fine-tuning improves accuracy on varEmotion by \(+5\%\), \(+14\%\), and \(+35\%\), respectively, relative to BaseNet; individual-level fine-tuning on \(\mathrm{varEmotion}_i\) yields further gains, including \(+3.5\%\) for DAN. For DAN, the Spearman correlation between model entropy \(H_m(x)\) and human entropy \(H_h(x)\) rises from \(\rho=0.26\) before fine-tuning to \(\rho=0.85\) after group fine-tuning [2507.14549].

The optimization used for alignment is ordinary cross-entropy,
\[
L_{\rm CE}(x,y)=-\sum_{k=1}^6 1_{[y=k]}\cdot \log p_k(x;\theta),
\]
minimized on the group mixture \(D_{\rm group}=\mathrm{RAF\text{-}DB}\cup \mathrm{varEmotion}\) at a \(1{:}2\) sample ratio and then on each individual dataset \(D_i=\mathrm{varEmotion}_i\cup \mathrm{varEmotion}\) at a \(2{:}1\) ratio. The reported optimizer is Adam with learning rate \(1\times 10^{-4}\), batch size \(128\), CrossEntropyLoss, and \(15\) epochs on an NVIDIA GPU [2507.14549].

## 5. Related boundary-based formulations

A distinct but technically related use of boundary samples appears in model watermarking. In iNNformant, a boundary sample for two inference environments \(A\) and \(B\) around a natural host sample \(x_0\) is an input \(x\) such that \(\|x-x_0\|\) is small and the final labels differ, \(y_A(x)\neq y_B(x)\) [2106.07303]. The paper defines \(m_A(x)\in \mathbb R^K\) as the softmax-vector output and
\[
d_{\rm confA}(x)=m_{A,(1)}(x)-m_{A,(2)}(x)
\]
as an approximate distance to the decision boundary on \(A\). A set of such samples is fully identifying for environments \(\{A_1,\dots,A_n\}\) if each \(A_i\) has at least one sample whose label differs from all others. The objective is therefore not annotation efficiency or human ambiguity, but identification of the execution environment through label instability near the boundary.

The optimization view is explicitly constraint-based: minimize perturbation magnitude subject to label disagreement across environments. Distortion is measured by PSNR,
\[
\mathrm{MSE}(\delta)=\frac{1}{d}\sum_{i=1}^d (\delta_i)^2,
\qquad
\mathrm{PSNR}(x,x_0)=20\log_{10}(MAX_I)-10\log_{10}(\mathrm{MSE}(\delta)).
\]
The generation algorithm uses a local phase to approach a decision boundary of a reference microarchitecture and a remote phase to refine the input until exactly one environment is isolated, using a modified FGSM-style update
\[
x^{t+1}=x^t+\alpha\, c\, d_{\rm conf\,ref}(x^t)\,\mathrm{sign}(\nabla_x m_{{\rm ref},(1)}(x^t)).
\]
On FMNIST with ResNet20 and CIFAR10 with ResNet32, success rates are reported as \(70.50\%\) and \(28.25\%\), respectively. By selecting the best PSNR sample per microarchitecture, the paper reports fully identifying sets whose worst PSNR exceeds \(70\,\mathrm{dB}\) on FMNIST or \(77\,\mathrm{dB}\) on CIFAR [2106.07303]. This suggests a boundary-sample regime in which perceptual fidelity is preserved, but the operative ambiguity is between hardware-specific executions rather than between semantic classes or between human observers.

An earlier and conceptually separate formulation is found in the literature on perceptual boundary saliency. There, the target is not a classifier’s decision frontier but the boundary of image level sets extracted by the Fast Level-Set Transform. A level line \(C\) of length \(\ell\) is declared \(\varepsilon\)-meaningful under the Helmholtz principle if its Number of False Alarms satisfies
\[
\mathrm{NFA}(C)=N_{ll}\Bigl[H_c\bigl(\min_{x\in C}|Du|(x)\bigr)\Bigr]^{\ell/2}<\varepsilon,
\]
where \(H_c(\mu)\) is an empirical tail histogram of gradient magnitudes and \(N_{ll}\) is the number of level lines [1210.3718]. The method extends earlier a-contrario formulations by allowing partially salient level lines rather than requiring an entire line to be salient.

The paper also introduces a regularity saliency at scale \(s\),
\[
R_s(x)=\frac{\max\{|x-C(\tau-s)|,\ |x-C(\tau+s)|\}}{s},
\]
and a combined saliency criterion denoted \(\mathrm{NFA}^{CR}_K(C)\), which relaxes punctual minima through percentile-based partial saliency. The detection algorithm computes the FLST, evaluates contrast and regularity statistics along each level line, marks curves as meaningful when their NFA is below \(\varepsilon\), and then performs maximality pruning along FLST branches. The total complexity is reported as approximately \(O(N\log N+N)\), with standard parameters \(\varepsilon=1\), \(K_c=K_s\approx 0.1n_C\), and \(s=5\) px [1210.3718].

Although this saliency-based work is not a decision-boundary method in the ANN sense, it is relevant for the broader semantics of perceptual boundaries. It treats perceptual significance as improbability under a null model and explicitly allows boundary point sampling on level lines for subsequent tasks such as shape matching, registration, stereo edge linking, and contour extraction [1210.3718].

## 6. Recurrent methodological themes, misconceptions, and open directions

A recurrent theme across these works is that boundary proximity alone is not considered sufficient. Each framework couples boundary seeking with an additional stabilizing mechanism. In BiLAF, uncertainty-oriented boundary selection is preceded by core selection for diversity and by IDC denoising to remove outliers before scoring [2403.10069]. In BAM and the facial-expression pipeline, the model boundary is accessed through a diffusion prior rather than direct pixel-space perturbation, precisely to keep the generated samples in-distribution and recognizable [2505.03641], [2507.14549]. In iNNformant, imperceptibility is enforced through a PSNR criterion, and in the saliency literature boundary detection is regularized by a-contrario thresholds, partial-saliency criteria, and maximality pruning [2106.07303], [1210.3718].

A common misconception is to equate boundary sampling with diversity sampling or with naïve uncertainty sampling. The surveyed literature separates these notions. BiLAF is explicitly bi-level: core sample selection covers the space, while boundary sample selection refines class frontiers [2403.10069]. BAM separates uncertainty guidance from controversial guidance, the latter being designed not merely to maximize entropy for one model but to induce disagreement between paired models and, later, between paired participant-specific models [2505.03641]. The facial-expression work similarly does not stop at balanced probabilities; it filters generated images by class-specific activation thresholds so that retained samples lie in a verified overlap region [2507.14549].

Another misconception is that “perceptual” always means human-defined. In several of these formulations, the perceptual substrate is initially ANN-internal: pretrained feature geometry in BiLAF, classifier posteriors in BAM, or emotion-class probabilities in varEmotion. Human perceptual variability enters only after behavioral validation and model alignment in the human-facing studies [2403.10069], [2505.03641], [2507.14549]. This suggests that current usage often begins with model-defined perceptual structure and then asks whether that structure predicts human ambiguity.

The open directions stated in these works are similarly heterogeneous. BAM proposes expansion beyond digit recognition to natural scenes, semantic tasks, and similarity judgments; incorporation of optimal experimental design loops, including active learning, to minimize human trials; and the study of cultural and developmental factors in more diverse participant populations [2505.03641]. The facial-expression study positions its findings as a route toward personalized modeling of emotional interpretation [2507.14549]. The saliency literature identifies corners and junctions, over-detection in textured areas, and multiscale fusion as unresolved issues [1210.3718]. The watermarking literature notes that scaling to higher-resolution inputs or deeper networks may require smaller step sizes or adaptive line search [2106.07303].

Taken together, these formulations establish perceptual boundary sampling as a boundary-centered design principle rather than a single canonical technique. Its modern forms range from sample-efficient active finetuning, through controlled synthesis of ambiguous stimuli for behavioral science, to imperceptible near-boundary perturbations and salient contour detection. The common structure is the deliberate exploitation of borderline cases, but the meaning of the boundary, the type of perceptual evidence, and the target downstream use remain domain-specific.

Source: https://www.emergentmind.com/topics/perceptual-boundary-sampling