Related Experiment Video

Updated: Jun 13, 2026

Photorealistic Learned Landscapes for Augmented Reality
06:54

Photorealistic Learned Landscapes for Augmented Reality

Published on: June 27, 2025

Least-squares reconstruction of spatially limited objects using smoothness and non-negativity constraints

Y Zhou, C K Rushforth

    Applied Optics
    |April 15, 2010
    PubMed

    Related Concept Videos

    Residuals and Least-Squares Property01:11

    Residuals and Least-Squares Property

    The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
    If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
    The process of fitting the best-fit...
    Curvilinear Motion: Rectangular Components01:23

    Curvilinear Motion: Rectangular Components

    Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
    As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...
    Lagrange Multipliers: Two Constraints01:28

    Lagrange Multipliers: Two Constraints

    The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.
    Calibration Curves: Linear Least Squares01:20

    Calibration Curves: Linear Least Squares

    A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
    For data that follow a straight line, the standard method for fitting is the linear...
    Linear Approximations01:23

    Linear Approximations

    For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
    Lagrange Multipliers: One Constraint01:29

    Lagrange Multipliers: One Constraint

    In constrained optimization, the objective is to maximize or minimize a quantity while satisfying a fixed condition. A standard example is a rectangular pen built against a barn wall using 100 meters of fencing. Because the wall provides one side of the enclosure, only the other three sides require fencing. The problem is to find the dimensions that produce the greatest possible area.Let L represent the length parallel to the wall and W the width perpendicular to it. The area of the pen is A =...