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Sawon Pratiher

Publications and source records attributed to Sawon Pratiher.

10 recordsLinked to original sources

Multi-Scale Fruit Capsules: Dilated Convolutions and Dynamic Routing for In-the-Wild Explainable Fruit Recognition

The same fruit appears in a bunch, unpicked, peeled, bagged in plastic, or sliced on a dish, so automated fruit classification in the wild (AFCW) must absorb wide intra- class and narrow inter-class variability in shape, size, colour and texture. Convolutional networks route information through pooling, which discards the pose and location of the region of interest and therefore generalises poorly across these presentations. We propose FruitCapsNet, a capsule network whose Fruit Capsules replace the standard convolutional front end with dilated convolutions: the receptive field grows exponentially at constant parameter cost, so each capsule encodes multi-scale context before dynamic routing resolves part whole spatial agreement. Hyper-parameters, including the dilation factor, are selected by Bayesian optimisation rather than grid search. On three public datasets (SMP, FruitsGB, Fruits-360) and a new 19-class, 10,639-image in-the-wild dataset (PD-19), FruitCapsNet exceeds ten fine-tuned transfer-learning backbones at one-third the depth, with the largest margin (+2.7% over the nearest competitor) on the hardest set. Grad-CAM saliency propagated from the DigitCaps layer shows that the improvement comes from attributing decisions to whole-fruit regions rather than to object edges, giving post-hoc evidence that the gain is not a dataset artefact.

cs.CV

A Simple Trigonometric Classification of Quintic Roots

This article provides a simple trigonometric method for determining how many roots of a quintic equation are real and how many are complex, without solving the equation. The approach transforms a depressed quintic $t^5 + mt^3 + nt^2 + pt + q = 0$ with $m < 0$ into the trigonometric equation $f(θ) = α\cos^2\!θ+ β\cosθ+ \cos 5θ+ γ= 0$ via the Chebyshev identity $16\cos^5\!θ- 20\cos^3\!θ+ 5\cosθ= \cos 5θ$. The derivation is computationally light and conceptually natural, extending the quartic case to fifth-degree equations. As the Abel--Ruffini theorem forbids a general algebraic solution for the quintic, having a simple trigonometric criterion for the nature of its roots is especially appealing.

math.NA

Recurrence Structures, Finite State Decomposition, and Statistical Bias in Collatz Path Sequences

We investigate the structure of Collatz path sequences $\{F^k(n)\}_{k=0}^{\infty}$ for positive integers $n$, where $F$ denotes the standard Collatz map. By classifying natural numbers into residue classes modulo~4, we establish that the Collatz conjecture reduces to verifying convergence for integers congruent to $3 \pmod{4}$. For this class, we identify six recurrent forms -- residue classes modulo~9 -- through which the path sequence elements cycle, and we prove that these forms are \emph{complete} in the sense that every power of~2 belongs to exactly one of them. We construct a deterministic finite state machine (FSM) whose states correspond to these six forms and whose transitions encode the Collatz dynamics, yielding a system of coupled functional equations involving linear congruences. We prove closed-form characterizations of the power-of-2 elements within three of the six recurrent classes and establish an equivalence between the FSM dynamics and the Syracuse acceleration of the Collatz map. Numerical experiments on the first $10^8$ natural numbers reveal a pronounced statistical bias in the distribution of terminating recurrent forms, with form $9n+8$ accounting for approximately $97.6\%$ of all terminations, and we formulate precise conjectures regarding the asymptotic frequencies. These results provide a structured decomposition of the Collatz problem into a finite system of interlocking recurrences and highlight the non-random character of the Collatz dynamics.

math.GM

A Simple Trigonometric Classification of Quartic Roots

This article provides a simple trigonometric method for determining how many roots of a quartic equation are real and how many are complex, without solving the equation. The approach replaces the quartic's classical discriminant -- a degree-six polynomial in the coefficients -- with an elementary analysis of the function $f(θ) = a\cosθ+ \cos 4θ+ b$ on $[0,π]$, obtained by matching the quartic to the Chebyshev identity $8\cos^4\!θ- 8\cos^2\!θ+ 1 = \cos 4θ$. The derivation is computationally light and conceptually natural, and has the potential to demystify the geometry of a quartic equation's roots from a trigonometric perspective.

math.GM

Diving Deep onto Discriminative Ensemble of Histological Hashing & Class-Specific Manifold Learning for Multi-class Breast Carcinoma Taxonomy

Histopathological images (HI) encrypt resolution dependent heterogeneous textures & diverse color distribution variability, manifesting in micro-structural surface tissue convolutions. Also, inherently high coherency of cancerous cells poses significant challenges to breast cancer (BC) multi-classification. As such, multi-class stratification is sparsely explored & prior work mainly focus on benign & malignant tissue characterization only, which forestalls further quantitative analysis of subordinate classes like adenosis, mucinous carcinoma & fibroadenoma etc, for diagnostic competence. In this work, a fully-automated, near-real-time & computationally inexpensive robust multi-classification deep framework from HI is presented. The proposed scheme employs deep neural network (DNN) aided discriminative ensemble of holistic class-specific manifold learning (CSML) for underlying HI sub-space embedding & HI hashing based local shallow signatures. The model achieves 95.8% accuracy pertinent to multi-classification & 2.8% overall performance improvement & 38.2% enhancement for Lobular carcinoma (LC) sub-class recognition rate as compared to the existing state-of-the-art on well known BreakHis dataset is achieved. Also, 99.3% recognition rate at 200X & a sensitivity of 100% for binary grading at all magnification validates its suitability for clinical deployment in hand-held smart devices.

cs.CV

StationPlot: A New Non-stationarity Quantification Tool for Detection of Epileptic Seizures

A novel non-stationarity visualization tool known as StationPlot is developed for deciphering the chaotic behavior of a dynamical time series. A family of analytic measures enumerating geometrical aspects of the non-stationarity & degree of variability is formulated by convex hull geometry (CHG) on StationPlot. In the Euclidean space, both trend-stationary (TS) & difference-stationary (DS) perturbations are comprehended by the asymmetric structure of StationPlot's region of interest (ROI). The proposed method is experimentally validated using EEG signals, where it comprehend the relative temporal evolution of neural dynamics & its non-stationary morphology, thereby exemplifying its diagnostic competence for seizure activity (SA) detection. Experimental results & analysis-of-Variance (ANOVA) on the extracted CHG features demonstrates better classification performances as compared to the existing shallow feature based state-of-the-art & validates its efficacy as geometry-rich discriminative descriptors for signal processing applications.

eess.SP

SolarisNet: A Deep Regression Network for Solar Radiation Prediction

Effective utilization of photovoltaic (PV) plants requires weather variability robust global solar radiation (GSR) forecasting models. Random weather turbulence phenomena coupled with assumptions of clear sky model as suggested by Hottel pose significant challenges to parametric & non-parametric models in GSR conversion rate estimation. Also, a decent GSR estimate requires costly high-tech radiometer and expert dependent instrument handling and measurements, which are subjective. As such, a computer aided monitoring (CAM) system to evaluate PV plant operation feasibility by employing smart grid past data analytics and deep learning is developed. Our algorithm, SolarisNet is a 6-layer deep neural network trained on data collected at two weather stations located near Kalyani metrological site, West Bengal, India. The daily GSR prediction performance using SolarisNet outperforms the existing state of art and its efficacy in inferring past GSR data insights to comprehend daily and seasonal GSR variability along with its competence for short term forecasting is discussed.

cs.CV

Application of S-Transform on Hyper kurtosis based Modified Duo Histogram Equalized DIC images for Pre-cancer Detection

Our proposed hyper kurtosis based histogram equalized DIC images enhances the contrast by preserving the brightness. The evolution and development of precancerous activity among tissues are studied through S-transform (ST). The significant variations of amplitude spectra can be observed due to increased medium roughness from normal tissue were observed in time-frequency domain. The randomness and inhomogeneity of the tissue structures among human normal and different grades of DIC tissues is recognized by ST based timefrequency analysis. This study offers a simpler and better way to recognize the substantial changes among different stages of DIC tissues, which are reflected by spatial information containing within the inhomogeneity structures of different types of tissue.

cs.CV

A comparative study between proposed Hyper Kurtosis based Modified Duo-Histogram Equalization (HKMDHE) and Contrast Limited Adaptive Histogram Equalization (CLAHE) for Contrast Enhancement Purpose of Low Contrast Human Brain CT scan images

In this paper, a comparative study between proposed hyper kurtosis based modified duo-histogram equalization (HKMDHE) algorithm and contrast limited adaptive histogram enhancement (CLAHE) has been presented for the implementation of contrast enhancement and brightness preservation of low contrast human brain CT scan images. In HKMDHE algorithm, contrast enhancement is done on the hyper-kurtosis based application. The results are very promising of proposed HKMDHE technique with improved PSNR values and lesser AMMBE values than CLAHE technique.

cs.CV

Wavelet based approach for tissue fractal parameter measurement: Pre cancer detection

In this paper, we have carried out the detail studies of pre-cancer by wavelet coherency and multifractal based detrended fluctuation analysis (MFDFA) on differential interference contrast (DIC) images of stromal region among different grades of pre-cancer tissues. Discrete wavelet transform (DWT) through Daubechies basis has been performed for identifying fluctuations over polynomial trends for clear characterization and differentiation of tissues. Wavelet coherence plots are performed for identifying the level of correlation in time scale plane between normal and various grades of DIC samples. Applying MFDFA on refractive index variations of cervical tissues, we have observed that the values of Hurst exponent (correlation) decreases from healthy (normal) to pre-cancer tissues. The width of singularity spectrum has a sudden degradation at grade-I in comparison of healthy (normal) tissue but later on it increases as cancer progresses from grade-II to grade-III.

cs.CV