Circularity-invariant method for accurately determining the perimeter of a particle in a digital image

Abstract

Disclosed herein is a circularity-invariant method for accurately determining the perimeter of a particle in a digital image. Conventional pixel-based perimeter estimation methods overestimate curved boundaries due to rigid assignment of diagonal pixel distances (√2), leading to errors in circularity and derived shape parameters. The disclosed method segments the particle, identifies boundary pixels, classifies them as orthogonal or diagonal, and applies an adaptive corrective factor defined as 1 + (D / X × 0.414), where D is the number of diagonal pixels and X is the total boundary pixels. This adjustment mitigates systematic overestimation, ensuring accurate, rotation-invariant perimeter estimation. The method improves calculation of circularity, convexity and high sensitivity circularity (HSC). It is computationally efficient, resolution-independent, and suitable for integration into industrial imaging workflows across materials science, pharmaceuticals, and biomedical applications.

Description

[0001] BEFORE THE INTERNATIONAL BUREAU OF THE WORLD INTELLECTUAL PROPERTY ORGANIZATION NON-PROVISIONAL APPLICATION FOR PATENT PCT Rule 19.1 (a)(iii)

[0002] Title: “Circularity-invariant method for accurately determining the perimeter of a particle in a digital image”

[0003] Applicant: ImageProVision Technology Private Limited (IN)

[0004] 3rd Floor, DS IKON, Survey no 22, Laxman Nagar, Baner Pune, Maharashtra, India - 41 1045

[0005] Inventors: 1 ) Sandeep Arvind Kulkarni (IN)

[0006] D-203, Anjor, Baner, N.I.A., Pune, Maharashtra, India — 411045

[0007] 2) Neha Sagar Deshmukh (IN)

[0008] A-801 , Vascon Willows, Baner Balewadi Road, N.I. A., Pune, Maharashtra, India - 41 1045

[0009] 3) Anu Shivanand Raje (IN)

[0010] Vikas Nagar, Near Ganpati Temple, Kivale, Dehu road, Kivale, Dehu Road Gantt, Mawal, Pune, Maharashtra - 412101

[0011] 4) Mihir Milind Limaye (IN)

[0012] Sr. No. 128 / 2, Plot No. 65, Gharkulna, Navketan Society Lane 5, Kothrud, Pune City, Ex. Serviceman Colony, Maharashtra - 41 1038

[0013] Priority: IN 202421072061 filed on 24 / 09 / 2024

[0014] Attorney file ref.: IR7929

[0015] Attorney: Rohit Nitin Deshpande (IN)

[0016] Advocate (MAH / 4858 / 2012) & Patent Agent (IN / PA-1389)

[0017] Address for service: Rohit Nitin Deshpande

[0018] Inventillect Consultants, Office No. 307, Business Guild Condominium, Apex Colony, ILS Law College Road, Erandwane, Pune, Maharashtra, India - 41 1004 Email: rd@inventillect.com Phone: +91 -9422944630 *** Non-Provisional Application

[0019] Circularity-invariant method for accurately determining the perimeter of a particle in a digital image”

[0020] Cross references to related applications: This international application claims priority from Indian patent application No. 202421072061 filed on 24 / 09 / 2024 the entire contents of which are incorporated herein in their entirety by way of reference.

[0021] Field of the invention

[0022] The present invention relates to the field of digital image processing. More particularly, it concerns a computational method for accurately estimating the perimeter of an object represented in discrete pixel space, while applying corrective factors to account for circularity and diagonal adjacency, thereby ensuring reliable rotation-invariant perimeter estimation in particle analysis and related applications.

[0023] Definitions and interpretations

[0024] Before undertaking the detailed description of the invention below, it may be advantageous to set forth definitions of certain words or phrases used throughout this patent document: the terms “include” and “comprise,” as well as derivatives thereof, mean inclusion without limitation; the term “or” is inclusive, meaning and / or; the phrases “associated with” and “associated therewith,” as well as derivatives thereof, may mean to include, be included within, interconnect, with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, or the like; and certain definitions are set forth for this document, as follows: -

[0025] (a) “Discrete pixel space” refers to the grid-like arrangement of pixels constituting a digital image, where each pixel is a discrete unit of spatial representation.

[0026] (b) “Rule of Distance 1 ” refers to the principle wherein each orthogonally adjacent pixel is considered to be separated by a distance of 1 unit, while diagonally adjacent pixels are conventionally considered to be separated by \2 = 1 .414 units.

[0027] (c) “High Sensitivity Circularity (HSC)” refers to a refined parameter that quantifies circularity with enhanced sensitivity to deviations in contour accuracy.

[0028] (d) Circularity may be computed using definitions known in art, such as 4TTA / P24TTA / PA24TTA / P2 or alternatively 2nx,,A / P2nx,A / P2TT- A / P. In both formulations, perimeter overestimation directly underestimates circularity, which the present invention corrects.

[0029] Background of the invention & Description of related art

[0030] Accurate determination of particle perimeter is a fundamental step in quantitative image analysis across multiple scientific and industrial domains, including material sciences, cytology, biomedical imaging, and particle size characterization. Reliable perimeter measurements are essential because they directly influence the calculation of secondary descriptors such as circularity, aspect ratio, Convexity and shape factors, all of which are critical in the classification, quality control, and functional assessment of materials and biological entities.

[0031] Conventional approaches to perimeter determination in digital images typically involve edge detection followed by contour tracing. Once the boundary of a particle or object has been delineated, the perimeter is approximated by summing contributions of pixel- to-pixel transitions along the contour. A widely adopted method in this context is the Rule of Distance 1 , in which horizontal and vertical (orthogonal) pixel connections are assigned a unit distance of 1 , while diagonal pixel connections are assigned a distance of ^2 (approximately 1.414). This pixel-based metric reflects the discrete geometry of the image grid and provides a simple means of approximating perimeter length without resorting to continuous curve fitting.

[0032] However, the digital representation of curved or oblique boundaries introduces a fundamental source of error. Specifically, the pixelization of smooth circular or nearcircular contours results in an inflated proportion of diagonal pixel connections relative to the true underlying geometry. As a result, the contribution of diagonals in the Rule of Distance 1 systematically overestimates the true perimeter of such shapes. This discrepancy is not merely a localized error but propagates into global metrics of shape characterization.

[0033] For example, in circular particles, the measured perimeter frequently exceeds the theoretical circumference, thereby biasing derived parameters such as circularity, commonly computed (4TT X Area / Perimeter) and equivalent diameters (e.g., Feret’s diameter, Heywood diameter). Overestimated perimeters produce artificially reduced circularity values, potentially leading to misclassification of particles as irregular or non- spherical. Similarly, equivalent diameter measurements may deviate from the actual particle size, thereby reducing accuracy in applications that rely on precise dimensional analysis.

[0034] The root of overestimation lies in that digital diagonal transitions are treated as though they represent steep angular changes between contour segments. While this is justified in shapes like diamonds, where diagonals represent true sharp vertices, it is unjustified in circles and ellipses where diagonal pixel alignments merely approximate smooth curves. This misinterpretation causes perimeter inflation in circular boundaries.

[0035] Several alternative strategies have been proposed in the literature to address these issues, such as sub-pixel interpolation, spline-based contour fitting, and model-based shape reconstruction. While these methods can mitigate perimeter overestimation, they often introduce trade-offs in terms of computational complexity, sensitivity to noise, or dependence on prior assumptions about particle shape. As a result, a robust and computationally efficient method for accurate perimeter determination in pixel-based digital images remains an unresolved challenge in the art.

[0036] Prior art, to the extent surveyed, lists some scattered attempts to address the issues mentioned hereinabove. For example is US2003 / 0095710 A1 (filed 2001 , assigned to Mitutoyo Corporation) titled “Systems and methods for boundary detection in images” discloses morphological and edge-based image preprocessing techniques to enhance boundary detection before computing perimeters. While morphological processing can improve segmentation accuracy, the approach introduces significant computational overhead and still lacks inherent correction for the inflated contribution of diagonal pixels in curved contours.

[0037] US2010 / 0091104 A1 (filed 2007, assigned to Georgia Tech Research Corp) titled “Systems and methods for the measurement of surfaces” describes a portable, noncontact, hand-held device using optical triangulation and reference markers to measure real-world object boundaries (originally intended for wound surfaces). Although innovative in compensating for skew and distortion, it focuses on 3D surface measurement and does not address pixel-level curvature artifacts or digital-perimeter inflation, and is less applicable when only 2D digital image data are available.

[0038] US20080088704 A1 (filed 2006, Mitutoyo Corporation) titled “Method of making digital planimetry measurements on digital photographs” teaches a method that allows perimeter — and other planimetric — measurements on digital images by including a calibration object (like a ruler) in the image. The method enables drawing of linear, area, and circumference measurements from the calibrated image. However, because it relies purely on manual outlining and direct measurement (e.g., by painting or tracing), it does not compensate for perimeter overestimation caused by the inflation of diagonal pixel contributions in curved or near-circular shapes, nor does it incorporate any algorithmic correction that accounts for digital discretization effects.

[0039] GB2398379 A (filed circa late 1990s-2000s, originally by Amersham International pic or a related assignee) titled “Automated digital image analysis” teaches an automated method for detecting objects in a digital image, deriving object boundaries, and then computing statistical shape properties — including variability of areas and shapes — for objects such as cell nuclei. However, this method focuses on statistical shape assessment and morphological classification, and does not explicitly address the systematic overestimation of perimeter measurement due to use of orthogonal vs. diagonal pixel contributions, particularly for curved boundaries.

[0040] Therefore, what is needed in the art is a perimeter estimation method that overcomes the shortcomings of conventional pixel-based approaches and prior art techniques. Such a method should be computationally efficient to enable large-scale or real-time image analysis, while maintaining robustness against noise and contour irregularities. It should further exhibit rotational invariance, ensuring that perimeter estimates remain consistent regardless of object orientation. Importantly, the method should incorporate a circularity correction mechanism to mitigate the systematic inflation of perimeter length caused by diagonal pixel contributions in digital representations of curved boundaries. Finally, the method should operate effectively across varying image resolutions and a wide range of particle morphologies, without requiring manual calibration objects or complex pre-processing pipelines.

[0041] Technical issues on hand: The foregoing survey of existing methods and disclosures demonstrates that although various attempts have been made, none satisfactorily resolve the limitations associated with perimeter estimation in digital images. Accordingly, the technical issues that remain outstanding may be systematically enumerated, as set forth below. a) Computational inefficiency: Existing methods often rely on chain codes, spline fitting, or morphological preprocessing that increase processing time and complexity. b) Orientation bias: Pixel-based perimeter measures vary with object rotation due to anisotropy of grid representation. c) Diagonal inflation error: Digital curves with high curvature systematically overestimate perimeter length because diagonal steps are rigidly weighted by ^2. d) Resolution dependence: Accuracy degrades when resolution changes, as discretization artifacts scale non-linearly with pixel size. e) Preprocessing requirements: Several prior methods require calibration objects, smoothing, or other pre-processing, which add user intervention and reduce automation potential. f) Limited robustness to morphology: Current techniques struggle to maintain accuracy across diverse particle geometries, from circular to irregular.

[0042] State-of-art therefore, does not list a single effective solution embracing all considerations mentioned hereinabove, thus preserving an acute necessity-to-invent for the present inventor / s who, as result of focused research, has come up with novel solutions for resolving all needs once and for all. Work of the applicant / s hereof, specifically directed against the technical problems recited hereinabove and currently part of the public domain including earlier filed patent applications, is neither expressly nor impliedly admitted as prior art against the present disclosures.

[0043] In view of these shortcomings, it becomes imperative to devise a solution that is computationally efficient, orientation-invariant, and robust to variations in morphology and resolution. The objectives of the present invention are therefore formulated in direct response to the aforesaid problems, as detailed in the following section.

[0044] Objectives of the present invention

[0045] The present invention is identified in addressing at least all major deficiencies of art discussed in the foregoing section by effectively addressing the objectives stated under, of which:

[0046] It is a primary objective to provide a method for accurately determining the perimeter of a particle in a digital image by adaptively correcting the contribution of diagonally aligned pixels, thereby overcoming systematic overestimation inherent in prior art approaches.

[0047] It is another objective further to the aforesaid objective(s) that said method ensures correct estimation of circularity and other shape-dependent metrics by minimizing distortion due to digital discretization.

[0048] It is another objective further to the aforesaid objective(s) that said method delivers rotation-invariant perimeter estimation across particle orientations, thereby ensuring uniform accuracy irrespective of shape alignment within the image plane.

[0049] It is another objective further to the aforesaid objective(s) that said method achieves computational efficiency, reduces dependence on extensive preprocessing, and remains robust across variations in image resolution and particle morphology.

[0050] It is another objective further to the aforesaid objective(s) that said method is environmentally safe, commercially viable, sustainable, not unduly complex, expensive, nor dependent on highly skilled personnel or specialized equipment to implement, thereby rendering it suitable for broad-scale industrial deployment.

[0051] The manner in which the above objectives are achieved, together with other objects and advantages which will become subsequently apparent, reside in the detailed description set forth below in reference to the accompanying drawings and furthermore specifically outlined in the independent claims. Other advantageous embodiments of the invention are specified in the dependent claims.

[0052] Brief description of drawings

[0053] The present invention is explained herein under with reference to the following drawings, in which:

[0054] FIGURE 1 is a flowchart illustrating the perimeter estimation method of the present invention.

[0055] The above drawings are illustrative of particular examples of the present invention but are not intended to limit the scope thereof. The drawings are not to scale (unless so stated) and are intended for use solely in conjunction with their explanations in the following detailed description.

[0056] While the drawings serve to schematically illustrate embodiments of the invention, the essence of the inventive concept is better appreciated from the following statement of invention, which sets forth the core features and advantages in a consolidated manner.

[0057] Statement / Summary of the invention

[0058] The present invention, in fulfilment of the objectives hereinabove set forth, provides a method for accurately determining the perimeter of a particle in a digital image by segmenting the particle, identifying its boundary pixels, classifying said pixels into orthogonal and diagonal categories, and applying an adaptive corrective factor proportional to the proportion of diagonal pixels so that the effective diagonal contribution is reduced from the fixed 12 weighting of prior art to 1 + (D / X x 0.414), where D represents diagonal pixels and X the total perimeter pixels, thereby avoiding systematic overestimation in curved boundaries and ensuring accurate calculation of perimeter and secondary shape parameters such as circularity, convexity and high sensitivity circularity (HSC); the method is rotation-invariant, computationally efficient, sustainable, commercially viable, and operable without undue complexity, expense, or dependence on specialized equipment, and is thus a novel and inventive contribution with marked industrial applicability.

[0059] Detailed description

[0060] Principally, the general purpose of the present invention is to assess the deficiencies and shortcomings inherent in known perimeter estimation systems of the state of the art and to develop a novel method incorporating all available advantages of the known art while avoiding any of its disadvantages.

[0061] Accordingly, the disclosures herein are directed towards a circularity-invariant method for accurately determining the perimeter of a particle in a digital image, wherein boundary pixels are identified and classified into orthogonal and diagonal categories, and an adaptive corrective factor proportional to the proportion of diagonal pixels is applied so that their contribution is reduced from the rigid ^2 convention of prior art to a corrected value of 1 + (D / X x 0.414), where D represents the number of diagonal pixels and X the total boundary pixels, thereby mitigating overestimation of perimeters in curved shapes and ensuring accurate derivation of secondary parameters such as circularity, convexity and high sensitivity circularity (HSC); the method further achieves rotation-invariance, computational efficiency, sustainability, commercial viability, and ease of industrial implementation without undue complexity, cost, or dependence on specialized personnel or equipment.

[0062] Approach: The founding approach of the present invention resides in a critical recognition that conventional reliance upon the Rule of Distance 1 , wherein orthogonal pixel adjacency is treated as a unit length of 1 and diagonal adjacency as ^2 (=1 .414), intrinsically distorts perimeter estimation for curved or circular particles in discrete pixel space. This distortion arises because the digital representation of smooth curves disproportionately introduces diagonal pixel alignments, which, when rigidly weighted by ^2, lead to systematic overestimation of perimeter and consequent underestimation of circularity. The inventors, through empirical analysis and mathematical experimentation, discovered that the degree of overestimation correlates with the proportion of diagonal pixels relative to total boundary pixels, and that a proportional corrective adjustment to the diagonal contribution yields an accurate representation of the true perimeter in linear space. By defining a corrective factor equal to 1 + (D / X x 0.414), where D denotes the number of diagonal pixels and X the total boundary pixels, the invention achieves a dynamic recalibration of pixel contributions that is sensitive to particle morphology, inherently rotation-invariant, and computationally efficient. This founding approach forms the conceptual and technical basis of the disclosed method, ensuring that it captures the advantages of established digital image analysis while overcoming its long-standing deficiencies.

[0063] Preferred Embodiment / Best Mode of Carrying Out the Invention

[0064] In a preferred embodiment, the invention is carried out through a sequence of computational steps executed by a computer-implementable code / software, upon a digital image comprising at least one particle or object of interest. The process begins with acquisition of a digital image in grayscale or color, which is then subjected to segmentation by thresholding or equivalent binarization methods to isolate the particle from its background. Following segmentation, a contour detection algorithm is applied to identify boundary pixels of the particle.

[0065] Said boundary pixels are classified into orthogonal and diagonal categories by assessing the relative adjacency of each pixel in the contour. Orthogonal adjacency is assigned a fixed contribution of one unit distance, whereas diagonal adjacency is subjected to correction by means of the inventive factor. In this embodiment, the corrective factor is derived as 1 + (D / X x 0.414), where D represents the number of diagonal pixels and X represents the total boundary pixel count. The corrected distance contribution is multiplied with the number of diagonally aligned pixels, while orthogonal contributions are summed directly, thereby yielding the final perimeter length.

[0066] For illustrative purposes, consider a digital image of a circular particle with a boundary comprising 1 ,000 pixels, of which 400 are diagonally aligned. The corrective factor is calculated as 1 + (400 / 1000 x 0.414) = 1.166. The diagonal contribution is thus computed as 400 x 1.166 = 466.4 units, while the orthogonal contribution is 600 x 1 = 600 units, producing a total perimeter of 1 ,066.4 units. When compared against the true analytical circumference of the circle, the error margin remains below 5%, demonstrating the accuracy and reliability of the present method.

[0067] In its best mode, the invention is implemented as a software module written in a high- level language, Rust-integrated within a particle analysis suite. The module operates on binary images produced by conventional segmentation pipelines and outputs perimeter length, circularity, convexity and high sensitivity circularity (HSC) as parameters. The method is designed to be resolution-independent, operating efficiently on both high-resolution microscopy images and lower-resolution industrial inspection frames.

[0068] This embodiment ensures computational efficiency by avoiding reliance on contour smoothing, spline interpolation, or other resource-intensive methods of the prior art, while delivering robustness against variations in particle orientation, thereby demonstrating the practical utility of the founding approach in real-world applications.

[0069] In furtherance of the preferred embodiment, the present invention contemplates further processing steps whereby the corrected perimeter values obtained through the inventive method are utilized to generate higher-order morphological and dimensional parameters that are critical in particle analysis. These include, without limitation, the computation of circularity, aspect ratio, elongation, area-equivalent diameters, and high sensitivity circularity (HSC). Each of these parameters is derived with improved accuracy owing to the corrected perimeter estimation, thereby overcoming distortions typically introduced by rigid diagonal weighting in the state of the art. This processing further enables characterization of products across diverse domains. In material sciences, the corrected parameters assist in determining grain structure, particle uniformity, and distribution, directly impacting quality control of alloys, ceramics, and powders. In pharmaceuticals, the method contributes to accurate assessment of particle size distributions of active ingredients and excipients, ensuring compliance with pharmacopeial standards. In biological sciences, improved circularity measurement assists in morphological classification of cells, microorganisms, and tissue structures, supporting diagnostic and research outcomes.

[0070] Characterization through the present invention may be implemented as part of automated inspection systems wherein the corrected perimeter data feeds into machine learning or statistical modules for classification and decision-making. The inventive method thus ensures that downstream analytical conclusions are based on reliable geometric metrics, minimizing error propagation and enhancing the fidelity of the overall product characterization workflow.

[0071] Hardware: An exemplary building list of materials for implementing the present invention is summarized in Table 1 below.

[0072] Table 1.

[0073] The following description explains how these hardware components are integrated within the imaging station to create a coherent and reliable apparatus.

[0074] Assembly: For practical enablement, the invention is implemented through an integrated assembly comprising optical, imaging, computational, and software subsystems arranged in a manner to facilitate the acquisition and analysis of particle images for perimeter determination. The assembly includes a high-resolution digital camera operatively coupled with a microscope or optical lens system, said combination being configured to acquire magnified and sharply resolved digital images of particles under investigation. The optical unit is connected to an image acquisition interface, such as a USB 3.0 or PCIe-based frame grabber, ensuring transfer of image data at high bandwidth and without loss of fidelity.

[0075] The captured image stream is transmitted to a processing unit, typically a workstation equipped with a multi-core CPU and optionally a GPU acceleration module, wherein the inventive algorithm is executed. The computational unit further comprises memory for storing intermediate datasets, a high-capacity storage device for archiving captured and processed images, and a display monitor for rendering real-time analytical outputs. The inventive method is embodied in a software environment such as Python, C++ or MATLAB, incorporating standard image processing libraries including OpenCV, NumPy, and SciPy, with the inventive corrective perimeter algorithm implemented therein as a module or routine.

[0076] The assembly thus ensures that each hardware component operates in conjunction with the inventive algorithm to enable accurate, rotation-invariant perimeter estimation. The configuration is modular, permitting adaptation to different industrial or research requirements, and scalable for both laboratory-scale and production-scale implementations. By virtue of its design, the assembly is commercially viable, environmentally safe, and does not depend on unduly specialized equipment or highly skilled personnel, thereby rendering the invention fully enabled and industrially applicable.

[0077] Operating Procedure: As seen in the accompanying FIGURE 1 , the process of this invention begins by identifying particle contour points and classifying boundary pixels into orthogonal (horizontal / vertical) and diagonal categories. Orthogonal pixels are summed directly, while diagonal pixels are corrected using a factor proportional to their proportion in the contour (1 + D / X x 0.414). The contributions are then combined to yield the corrected perimeter of the particle, ensuring rotation invariance and eliminating systematic overestimation present in conventional methods. Accordingly, the operations of the present invention may be carried out in accordance with the following procedural steps, which are illustrative of the best mode of implementing the disclosed method:

[0078] Step 1 : Image Acquisition: A digital image of the particle or object of interest is captured using a high-resolution camera, optionally coupled with an optical or microscopic assembly, and transferred to the processing unit via an image acquisition interface.

[0079] Step 2: Pre-processing and Segmentation: The acquired image is converted into grayscale if necessary, and subjected to binarization or thresholding to segment the particle from the background. Noise reduction filters may be applied to improve clarity of the particle boundary. Step 3: Contour Detection: The segmented image is analyzed using a contour detection algorithm to identify boundary pixels of the particle in discrete pixel space. The identified pixels are then arranged into a closed boundary representation.

[0080] Step 4: Classification of Pixels: The boundary pixels are classified into orthogonal pixels (adjacent horizontally or vertically) and diagonal pixels (adjacent diagonally) based on their relative adjacency.

[0081] Step 5: Application of Corrective Factor: The proportion of diagonal pixels (D) to the total number of perimeter pixels (X) is determined. A corrective factor is computed as 1 + (D / X x 0.414). Each diagonal pixel’s contribution is weighted by this corrective factor, while orthogonal pixels are assigned a contribution of 1 .

[0082] Step 6: Perimeter Calculation: The corrected contributions of diagonal and orthogonal pixels are summed to obtain the true perimeter length of the particle.

[0083] Step 7: Derivation of Shape Parameters: Using the corrected perimeter, higher-order parameters such as circularity, convexity and high sensitivity circularity (HSC) are derived with improved accuracy.

[0084] Step 8: Output and Analysis: The calculated perimeter and associated shape parameters are stored in digital memory, displayed on a monitor, and optionally exported for downstream analysis in quality control, diagnostics, or research applications.

[0085] Experimental Validation: Experimental validation was performed across multiple geometric shapes — circle, square, diamond, and ellipse — at varying pixel resolutions. Results consistently showed that the corrected perimeter deviated by less than 5% from the theoretical values across all shapes and orientations, whereas the prior art Rule-of-Distance-1 consistently overestimated perimeter. Representative results are tabulated below.

[0086] Table 3 summarizes the comparative error margins (%) for key morphological descriptors, including length, width, aspect ratio, elongation, perimeter, area, circleequivalent diameter (CED), shape-equivalent volume (SEV), circularity, and Haralick shape coefficient (HSC). The data demonstrate that the present method achieves accuracy and rotation invariance across morphologies.

[0087] Table 3.

[0088] Comparative Studies: Benchmarks were performed against the conventional Rule-of- Distance-1 perimeter estimation method. As is well-known, RoD-1 systematically overestimates perimeters for curves and oblique edges, yielding errors exceeding 10% for circular and elliptical shapes, and inconsistent values under rotation. In contrast, the present Diagonal Factor approach consistently reduced perimeter error to below 5%, while maintaining accuracy for shapes with sharp angles such as squares and diamonds.

[0089] Representative comparative results are presented in Table 4 below. These data demonstrate not only error reduction across curved geometries but also rotation invariance, thereby confirming that the invention achieves systematic improvement over prior art methods without introducing new deficiencies.

[0090]

[0091] Table 4.

[0092] As observed above, curved shapes such as circles and ellipses exhibited perimeter overestimates exceeding 10% under the conventional Rule-of-Distance-1 method, whereas the Diagonal Factor approach consistently reduced error below 5% and often below 2% at higher resolutions. For polygonal shapes with sharp corners, including squares and diamonds, both methods performed comparably, with no loss of accuracy attributable to the Diagonal Factor correction. Furthermore, while RoD-1 values fluctuated with object orientation — particularly for ellipses — the present method demonstrated rotation invariance, yielding consistent results regardless of shape orientation.

[0093] These comparative benchmarks, together with the systematic validation data presented above, establish a clear performance improvement over the Rule-of- Distance-1 method in both accuracy and invariance, thereby providing the technical foundation for the inventive step discussed below.

[0094] The experimental validation and comparative benchmarks thus provide empirical evidence of the efficacy of the disclosed method. Against this backdrop of demonstrable improvement, the novelty and inventive step of the present invention are now articulated in the context of prior teachings.

[0095] Novelty and Inventive Step: As shown in the Comparative Results section, the claimed Diagonal Factor method systematically improves upon the conventional Rule- of-Distance-1 by reducing perimeter error from values exceeding 10% to consistently less than 5%, without loss of accuracy for sharp-cornered shapes and with full rotation invariance. This constitutes a distinct technical advance over prior art, which is prone to systematic overestimation and orientation-dependent inconsistencies.

[0096] The present invention is distinguished from the known art by its introduction of an adaptive corrective factor into perimeter calculation within discrete pixel space. Prior art systems uniformly apply the Rule of Distance 1 , wherein orthogonal pixels are assigned a distance of 1 and diagonal pixels a distance of >12, irrespective of particle morphology. This rigid assignment results in consistent overestimation of perimeters for curved shapes and consequent underestimation of circularity. The inventive method departs from such convention by recognizing that the proportion of diagonal pixels to total perimeter pixels directly influences the magnitude of overestimation, and by formulating a corrective factor expressed as 1 + (D / X x 0.414), where D is the number of diagonal pixels and X the total boundary pixels.

[0097] This adaptive correction achieves rotation-invariance, as experimental evidence demonstrates that shapes of identical morphology but varying angular orientation yield consistent perimeter values when processed under the inventive scheme. Unlike prior art, which often compensates inaccuracies through complex contour smoothing, spline fitting, or statistical averaging — approaches that increase computational burden without eliminating systematic bias — the present invention provides an elegant mathematical correction that is both computationally efficient and empirically validated.

[0098] The inventive step is therefore evident in the recognition of diagonal pixel proportion as a critical determinant of perimeter error, the translation of that recognition into a corrective mathematical model, and the realization of this model into a functional algorithm that significantly improves accuracy in perimeter estimation and derived shape parameters. Such a contribution is not taught, suggested, or rendered obvious by any of the cited prior art references.

[0099] Empirical tests disclosed in this document confirmed that identical shapes rotated at varying orientations yield consistent perimeter values, thereby evidencing true rotation invariance of the proposed corrective factor.

[0100] Having delineated the novelty and inventive step, it is instructive to further demonstrate how the present invention systematically scores above and beyond the cumulative teachings of the prior art, as discussed below.

[0101] Scoring Above the Teachings of the Art: When evaluated against the teachings of known art, the present invention demonstrably scores above in several respects. Conventional systems for perimeter estimation in digital images rely upon fixed assignment of distances for orthogonal and diagonal pixel adjacencies, thereby inheriting inaccuracies when applied to curved or circular boundaries. Known approaches often attempt to mitigate these errors through contour smoothing, spline fitting, or morphological processing, yet these measures increase computational complexity, remain resolution-dependent, and fail to directly address the fundamental cause of overestimation.

[0102] The present invention overcomes such deficiencies by introducing an adaptive corrective factor that proportionally adjusts the contribution of diagonal pixels relative to their prevalence in the boundary. This innovation directly resolves the inherent distortion caused by discrete pixel representation of curved shapes, while simultaneously achieving rotation invariance so that perimeter values remain consistent irrespective of particle orientation. The correction is mathematically precise, computationally efficient, and readily integrable into existing image analysis pipelines without requiring extensive preprocessing or specialized hardware.

[0103] Accordingly, the inventive method embodies a higher technical effect than known art: accurate perimeter estimation with significantly reduced error margins, robust and reliable derivation of secondary shape parameters such as circularity and equivalent diameters, and adaptability across a broad range of particle morphologies, sizes, and resolutions. These advancements collectively evidence both novelty and inventive step, as they represent a distinct and non-obvious improvement beyond the cumulative teachings of the art.

[0104] Thus to summarize, the present invention achieves a distinct technical advancement over known systems by introducing a corrective factor that proportionally adjusts the contribution of diagonally aligned pixels in perimeter estimation, thereby directly eliminating the root cause of systematic overestimation in curved particle boundaries. Unlike conventional methods that rely on fixed distance assignments or computationally intensive contour refinements, the invention provides a mathematically adaptive yet computationally efficient approach that ensures accuracy, rotation invariance, and consistency across diverse particle morphologies and resolutions. This advancement results in significantly reduced error margins, reliable derivation of circularity and equivalent diameters, and seamless integration into industrial imaging workflows, thereby evidencing a technical effect and industrial applicability not taught or suggested by the art. Importantly, the present invention is not a mere mathematical method, algorithm, or computer program per se within the meaning of Section 3 of the Patents Act, 1970, but instead constitutes a technical solution to a technical problem. The invention is directed towards correcting deficiencies in digital image perimeter estimation by introducing a novel corrective factor applied to discrete pixel representations, which is a concrete technical improvement over conventional system. The inventive method is inseparably tied to image acquisition hardware, processing units, and downstream analytical workflows, and its implementation produces a tangible technical effect in the form of enhanced accuracy, rotation-invariant perimeter estimation, and reliable derivation of shape parameters. The disclosures herein thus demonstrate an invention with industrial applicability, technical advancement, and practical utility, rather than a mere abstract algorithm. Furthermore, the invention is fully compliant with the CRI Guidelines issued by the Indian Patent Office, as it clearly identifies hardware components, demonstrates a specific technical effect, and is industrially deployable across fields such as metallurgy, pharmaceuticals, and biological imaging. Accordingly, the subject matter of the present application falls outside the prohibitions of Section 3(k) and is patent-eligible under the prevailing statutory framework.

[0105] The foregoing discussion establishes the technical advancement of the present invention. It is equally important to underscore its broad industrial applicability across scientific, medical, and commercial domains, as elaborated hereunder.

[0106] Industrial Applicability: The invention is industrially applicable across multiple domains wherein particle characterization by image analysis is a critical requirement. In materials science and metallurgy, the invention facilitates accurate determination of grain size distributions, phase structures, and particulate morphology, directly informing quality control in alloy and ceramic manufacturing. In pharmaceuticals, it supports precise measurement of active ingredient and excipient particle sizes, ensuring batch-to-batch consistency and regulatory compliance under pharmacopeial standards. In environmental sciences, it enables reliable monitoring of particulate matter in air, soil, and water samples. In biomedical and life sciences, it enhances morphological classification of cells, tissues, and microorganisms, thereby improving diagnostic accuracy and supporting research in pathology and microbiology.

[0107] The computational efficiency of the method ensures scalability from laboratory-scale research systems to industrial production lines. By eliminating the need for highly

Claims

specialized equipment or excessive preprocessing, the invention reduces operational costs and broadens accessibility for diverse end-users. Its software-based implementation allows integration into existing digital imaging pipelines, inspection systems, and automated platforms, thereby ensuring seamless adoption in industrial workflows. As will be realized further, the present invention is capable of various other embodiments and that its several components and related details are capable of various alterations, all without departing from the basic concept of the present invention. Accordingly, the foregoing description will be regarded as illustrative in nature and not as restrictive in any form whatsoever. Modifications and variations of the system and apparatus described herein will be obvious to those skilled in the art. Such modifications and variations are intended to come within ambit of the present invention, which is limited only by the appended claims.Dated this 20thDay of September 2025Duly constituted agent for the applicant,Rohit Nitin DeshpandeAdvocate [MAH / 4858 / 2012] & Patent Agent [IN / PA-1389]Address for service: Inventillect Consultants, Office No. 307, Business Guild Condominium, Apex Colony, ILS Law College Road, Erandwane, Pune, Maharashtra, India - 411004 Phone: +91 -9422944630 Email: rd@inventillect.comClaimsWe claim,1] A method for determining a corrected perimeter of a particle in a digital image, the method comprising:(a) acquiring a digital image in grayscale or colour comprising at least one particle using an image acquisition unit;(b) performing preprocessing including at least one of binarization, thresholding, or noise reduction to segment the particle from a background region;(c) detecting a contour of the particle and identifying boundary pixels;(d) classifying the boundary pixels into orthogonal pixels and diagonal pixels based on adjacency;(e) computing a corrective factor as 1 + (D / X x 0.414), where D represents the number of diagonal pixels and X represents the total number of boundary pixels;(f) applying the corrective factor to adjust the contribution of the diagonal pixels;(g) summing the contributions of the orthogonal pixels and the adjusted diagonal pixels to thereby producing a corrected perimeter of the particle that is rotation-invariant irrespective of particle orientation and independent of digital image resolution; and(h) outputting the corrected perimeter and one or more shape parameters derived therefrom. wherein■ the corrected perimeter is consistent across different rotational orientations of the particle and across digital images of varying resolution, thereby achieving rotation-invariant and resolutionindependent perimeter determination without requiring calibration objects, contour smoothing, spline interpolation, or morphological preprocessing■ the corrected perimeter estimation achieves less than 5% error relative to analytical perimeter values across multiple particle morphologies.2] The method for determining a corrected perimeter of a particle in a digital image as claimed in Claim 1 , wherein the one or more shape parameterscomprise at least circularity, convexity, high sensitivity circularity, aspect ratio, elongation, one or more equivalent diameters, and Haralick shape coefficient. The method for determining a corrected perimeter of a particle in a digital image as claimed in Claim 1 , wherein the corrective factor is dynamically recomputed for each particle such that the method provides rotation-invariant perimeter determination across particle orientations and resolution independence across digital images of different pixel densities. The method for determining a corrected perimeter of a particle in a digital image as claimed in Claim 1 , wherein the corrected perimeter determination avoids reliance on spline interpolation, contour smoothing, or morphological preprocessing, thereby improving computational efficiency. A system for determining a corrected perimeter of a particle in a digital image, the system comprising:(a) an image acquisition unit comprising a digital camera and an optical lens assembly configured to capture images of particles;(b) an image acquisition unit comprising a digital camera operatively coupled with a microscope or optical lens assembly configured to magnify and capture images of particles;(c) the processing unit comprising a processor and optionally a graphics processing unit (GPU) configured to accelerate execution of image analysis and perimeter correction, and a memory storing instructions executable to:■ perform preprocessing to segment the particle from the background,■ detect a contour of the particle and identify boundary pixels,■ classify the boundary pixels into orthogonal and diagonal pixels,■ compute a corrective factor as 1 + (D / X x 0.414),■ apply the corrective factor to the diagonal pixels,■ compute the corrected perimeter of the particle, and■ derive one or more shape parameters using the corrected perimeter, the parameters comprising at least convexity, circularity, and high sensitivity circularity; and(d) an output interface configured to display, store, or export the corrected perimeter and shape parameters to downstream analysis applications.

Images