arXiv subjects

G. Ishikawa

Publications and source records attributed to G. Ishikawa.

6 recordsLinked to original sources

arXiv2020

Global Wheat Head Detection (GWHD) dataset: a large and diverse dataset of high resolution RGB labelled images to develop and benchmark wheat head detection methods

Detection of wheat heads is an important task allowing to estimate pertinent traits including head population density and head characteristics such as sanitary state, size, maturity stage and the presence of awns. Several studies developed methods for wheat head detection from high-resolution RGB imagery. They are based on computer vision and machine learning and are generally calibrated and validated on limited datasets. However, variability in observational conditions, genotypic differences, development stages, head orientation represents a challenge in computer vision. Further, possible blurring due to motion or wind and overlap between heads for dense populations make this task even more complex. Through a joint international collaborative effort, we have built a large, diverse and well-labelled dataset, the Global Wheat Head detection (GWHD) dataset. It contains 4,700 high-resolution RGB images and 190,000 labelled wheat heads collected from several countries around the world at different growth stages with a wide range of genotypes. Guidelines for image acquisition, associating minimum metadata to respect FAIR principles and consistent head labelling methods are proposed when developing new head detection datasets. The GWHD is publicly available at http://www.global-wheat.com/ and aimed at developing and benchmarking methods for wheat head detection.

cs.CV↗

arXiv2018

Leibniz complexity of Nash functions on differentiations

The derivatives of Nash functions are Nash functions which are derived algebraically from their minimal polynomial equations. In this paper we show that, for any non-Nash analytic function, it is impossible to derive its derivatives algebraically, i.e., by using linearity and Leibniz rule finite times. In fact we prove the impossibility of such kind of algebraic computations, algebraically by using K{\" a}hler differentials. Then the notion of Leibniz complexity of a Nash function is introduced in this paper, as a computational complexity on its derivative, by the minimal number of usages of Leibniz rules to compute the total differential algebraically. We provide general observations and upper estimates on Leibniz complexity of Nash functions, related to the binary expansions, the addition chain complexity, the non-scalar complexity and the complexity of Nash functions in the sense of Ramanakoraisina.

math.AG↗

arXiv2016

Singularities of tangent surfaces to directed curves

A directed curve is a possibly singular curve with well-defined tangent lines along the curve. Then the tangent surface to a directed curve is naturally defined as the ruled surface by tangent geodesics to the curve, whenever any affine connection is endowed with the ambient space. In this paper the local diffeomorphism classification is completed for generic directed curves. Then it turns out that the swallowtails and open swallowtails appear generically for the classification on singularities of tangent surfaces.

math.DG↗

arXiv2014

Duality on geodesics of Cartan distributions and sub-Riemannian pseudo-product structures

Given a five dimensional space endowed with a Cartan distribution, the abnormal geodesics form another five dimensional space with a cone structure. Then it is shown, if the cone structure is regarded as a control system, then, the space of abnormal geodesics of the cone structure is naturally identified with the original space. In this paper, we provide an exposition on the duality by abnormal geodesics in a wider framework, namely, in terms of quotients of control systems and sub-Riemannian pseudo-product structures. Also we consider the controllability of cone structures and describe the constrained Hamiltonian equations on normal and abnormal geodesics.

math.DG↗

arXiv2003

Infinitesimal deformations and stabilities of singular Legendre submanifolds

We give the characterization of Arnol'd-Mather type for stable singular Legendre immersions. The most important building block of the theory is providing a module structure on the space of infinitesimal integral deformations by means of the notion of natural liftings of differential systems and of contact Hamiltonian vector fields.

math.DG↗

arXiv2003

Generic singularities of implicit systems of first order differential equations on the plane

For the implicit systems of first order ordinary differential equations on the plane there is presented the complete local classification of generic singularities of family of its phase curves up to smooth orbital equivalence. Besides the well known singularities of generic vector fields on the plane and the singularities described by a generic first order implicit differential equations, there exists only one generic singularity described by the implicit first order equation supplied by Whitney umbrella surface generically embedded to the space of directions on the plane.

math.DS↗