arXiv subjects

Nehal Doiphode

Publications and source records attributed to Nehal Doiphode.

4 recordsLinked to original sources

arXiv2025

Holonomy, Zeta Functions, and Cohomological Structures in Foliated Manifolds with Stratified Boundaries

This paper explores the interplay between holonomy, Ihara zeta functions, and cohomological structures within the framework of ratified F-completions of foliated manifolds. We develop a novel formalism for the Gamma-set, a topological multigraph that captures intersection points of foliations with stratified boundaries, and use it to define an Ihara zeta function that encodes the manifold's symmetries. By investigating the holonomy group of spinor fields in relation to the Delta-actions on the Gamma-set, we conjecture a duality between holonomy fixed points and the poles of the Ihara zeta function, extending to twisted cohomology classes. We further analyze how the twist map T impacts cohomology within stratified spaces, highlighting the role of vector bundles and the twisted cochain complex. Applications of our framework to spectral graph theory and tiling in R^n demonstrate the power of holonomy-zeta duality in geometrically rich foliated structures.

math.GT↗

arXiv2022

Beyond mAP: Towards better evaluation of instance segmentation

Correctness of instance segmentation constitutes counting the number of objects, correctly localizing all predictions and classifying each localized prediction. Average Precision is the de-facto metric used to measure all these constituents of segmentation. However, this metric does not penalize duplicate predictions in the high-recall range, and cannot distinguish instances that are localized correctly but categorized incorrectly. This weakness has inadvertently led to network designs that achieve significant gains in AP but also introduce a large number of false positives. We therefore cannot rely on AP to choose a model that provides an optimal tradeoff between false positives and high recall. To resolve this dilemma, we review alternative metrics in the literature and propose two new measures to explicitly measure the amount of both spatial and categorical duplicate predictions. We also propose a Semantic Sorting and NMS module to remove these duplicates based on a pixel occupancy matching scheme. Experiments show that modern segmentation networks have significant gains in AP, but also contain a considerable amount of duplicates. Our Semantic Sorting and NMS can be added as a plug-and-play module to mitigate hedged predictions and preserve AP.

cs.CV↗

arXiv2018

An Improved Learning Framework for Covariant Local Feature Detection

Learning feature detection has been largely an unexplored area when compared to handcrafted feature detection. Recent learning formulations use the covariant constraint in their loss function to learn covariant detectors. However, just learning from covariant constraint can lead to detection of unstable features. To impart further, stability detectors are trained to extract pre-determined features obtained by hand-crafted detectors. However, in the process they lose the ability to detect novel features. In an attempt to overcome the above limitations, we propose an improved scheme by incorporating covariant constraints in form of triplets with addition to an affine covariant constraint. We show that using these additional constraints one can learn to detect novel and stable features without using pre-determined features for training. Extensive experiments show our model achieves state-of-the-art performance in repeatability score on the well known datasets such as Vgg-Affine, EF, and Webcam.

cs.CV↗

arXiv2018

A Large Dataset for Improving Patch Matching

We propose a new dataset for learning local image descriptors which can be used for significantly improved patch matching. Our proposed dataset consists of an order of magnitude more number of scenes, images, and positive and negative correspondences compared to the currently available Multi-View Stereo (MVS) dataset from Brown et al. The new dataset also has better coverage of the overall viewpoint, scale, and lighting changes in comparison to the MVS dataset. Our dataset also provides supplementary information like RGB patches with scale and rotations values, and intrinsic and extrinsic camera parameters which as shown later can be used to customize training data as per application. We train an existing state-of-the-art model on our dataset and evaluate on publicly available benchmarks such as HPatches dataset and Strecha et al.\cite{strecha} to quantify the image descriptor performance. Experimental evaluations show that the descriptors trained using our proposed dataset outperform the current state-of-the-art descriptors trained on MVS by 8%, 4% and 10% on matching, verification and retrieval tasks respectively on the HPatches dataset. Similarly on the Strecha dataset, we see an improvement of 3-5% for the matching task in non-planar scenes.

cs.CV↗