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Lecture# Resizing, Interpolation and Image Math Introduction

Description

This lecture introduces the concepts of resizing images and interpolation, providing guidelines for determining the optimal pixel size based on specific features. Additionally, the instructor covers basic mathematical operations applicable to images, showcasing practical examples.

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BIO-695: Image Processing for Life Science

Registration details will be announced via email. It takes place from September to December & intends to teach image processing with a strong emphasis of applications in life sciences. The idea is to

Image Processing and Analysis for Life Scientists

This course intends to teach image analysis/processing with a strong emphasis
of applications in life sciences. The idea is to enable the participants to solve
image processing questions via workflo

Image Processing and Analysis for Life Scientists

This course intends to teach image analysis/processing with a strong emphasis
of applications in life sciences. The idea is to enable the participants to solve
image processing questions via workflo

Interpolation

In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable.

Multivariate interpolation

In numerical analysis, multivariate interpolation is interpolation on functions of more than one variable (multivariate functions); when the variates are spatial coordinates, it is also known as spatial interpolation. The function to be interpolated is known at given points and the interpolation problem consists of yielding values at arbitrary points . Multivariate interpolation is particularly important in geostatistics, where it is used to create a digital elevation model from a set of points on the Earth's surface (for example, spot heights in a topographic survey or depths in a hydrographic survey).

Polynomial interpolation

In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. Given a set of n + 1 data points , with no two the same, a polynomial function is said to interpolate the data if for each . There is always a unique such polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials.

Bilinear interpolation

In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals. Bilinear interpolation is performed using linear interpolation first in one direction, and then again in another direction.

Nearest-neighbor interpolation

Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is the problem of approximating the value of a function for a non-given point in some space when given the value of that function in points around (neighboring) that point. The nearest neighbor algorithm selects the value of the nearest point and does not consider the values of neighboring points at all, yielding a piecewise-constant interpolant.