EFFICIENT ALGORITHMS FOR OPTIMIZATION-BASED IMAGE SEGMENTATION

2001 ◽  
Vol 11 (02) ◽  
pp. 145-166 ◽  
Author(s):  
TETSUO ASANO ◽  
DANNY Z. CHEN ◽  
NAOKI KATOH ◽  
TAKESHI TOKUYAMA
Keyword(s):  
Optimization Problem ◽  
Approximation Scheme ◽  
Connected Region ◽  
Polynomial Time Algorithms ◽  
Optimization Formulation ◽  
Point Set ◽  
Fixed Constant ◽  
Optimal Segmentation ◽  
Efficient Approximation ◽  
Segmentation Problem

Separating an object in an image from its background is a central problem (called segmentation) in pattern recognition and computer vision. In this paper, we study the computational complexity of the segmentation problem, assuming that the sought object forms a connected region in an intensity image. We show that the optimization problem of separating a connected region in a grid of N×N pixels is NP-hard under the interclass variance, a criterion that is often used in discriminant analysis. More importantly, we consider the basic case in which the object is bounded by two x-monotone curves (i.e., the object itself is x-monotone), and present polynomial-time algorithms for computing the optimal segmentation. Our main algorithm for exact optimal segmentation by two x-monotone curves runs in O(N4) time; this algorithm is based on several techniques such as a parametric optimization formulation, a hand-probing algorithm for the convex hull of an unknown planar point set, and dynamic programming using fast matrix searching. Our efficient approximation scheme obtains an ∊-approximate solution in O(∊-1 N2 log L) time, where ∊ is any fixed constant with 1>∊>0, and L is the total sum of the absolute values of the brightness levels of the image.

Determination of the Interference Distance Between Two Objects Using Optimization Techniques

1994 ◽  
Author(s):  
Meyer Nahon
Keyword(s):  
Optimization Problem ◽  
Accurate Determination ◽  
Separation Distance ◽  
Optimization Techniques ◽  
Robotic Systems ◽  
Separation Problem ◽  
Optimization Formulation ◽  
Minimum Separation ◽  
Two Bodies

Abstract The determination of the interference distance between objects is a problem encountered in the off-line simulation of robotic systems. It is similar to the problem of finding the minimum separation distance between two bodies — a problem which, at present, is commonly solved using optimization techniques. This paper presents an analogous optimization formulation for the quick and accurate determination of the interference distance between two interfering objects. The optimization problem consists of finding the maximum amount by which the boundaries of two interfering object can be moved back while still maintaining a non-empty interference volume. Since the approach used is similar to that used in the minimum separation problem, a single algorithm has been implemented which, given the position and orientation of two objects, will return the separation or interference distance between the objects, as appropriate.

Assortment Optimization Under the Multinomial Logit Model with Sequential Offerings

2020 ◽  
Vol 32 (3) ◽  
pp. 835-853 ◽  
Author(s):  
Nan Liu ◽  
Yuhang Ma ◽  
Huseyin Topaloglu
Keyword(s):  
Logit Model ◽  
Optimization Problem ◽  
Approximation Scheme ◽  
Optimization Problems ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Polynomial Time Approximation Scheme ◽  
Assortment Optimization ◽  
Last Stage ◽  
Expected Revenue

We consider assortment optimization problems, where the choice process of a customer takes place in multiple stages. There is a finite number of stages. In each stage, we offer an assortment of products that does not overlap with the assortments offered in the earlier stages. If the customer makes a purchase within the offered assortment, then the customer leaves the system with the purchase. Otherwise, the customer proceeds to the next stage, where we offer another assortment. If the customer reaches the end of the last stage without a purchase, then the customer leaves the system without a purchase. The choice of the customer in each stage is governed by a multinomial logit model. The goal is to find an assortment to offer in each stage to maximize the expected revenue obtained from a customer. For this assortment optimization problem, it turns out that the union of the optimal assortments to offer in each stage is nested by revenue in the sense that this union includes a certain number of products with the largest revenues. However, it is still difficult to figure out the stage in which a certain product should be offered. In particular, the problem of finding an assortment to offer in each stage to maximize the expected revenue obtained from a customer is NP hard. We give a fully polynomial time approximation scheme for the problem when the number of stages is fixed.

Cost Minimum Proportioning of Non-Slump Concrete Mix Using Genetic Algorithms

2012 ◽  
Vol 468-471 ◽  
pp. 50-54 ◽  
Author(s):  
Md. Moshiur Rahman ◽  
Mohd Zamin Jumaat
Keyword(s):  
Compressive Strength ◽  
Optimization Problem ◽  
Constrained Optimization Problem ◽  
Nonlinear Constrained Optimization ◽  
Constituent Material ◽  
Optimization Formulation ◽  
Materials Used ◽  
The Individual ◽  
The Cost ◽  
Optimal Quantity

This paper presents a generalized formulation for determining the optimal quantity of the materials used to produce Non-Slump Concrete with minimum possible cost. The proposed problem is formulated as a nonlinear constrained optimization problem. The proposed problem considers cost of the individual constituent material costs as well as the compressive strength and other requirement. The optimization formulation is employed to minimize the cost function of the system while constraining it to meet the compressive strength and workability requirement. The results demonstrate the efficiency of the proposed approach to reduce the cost as well as to satisfy the above requirement.

A nonlinear optimization shooting method for bifurcation tracking of nonlinear systems

2020 ◽  
pp. 107754632095674
Author(s):  
Haitao Liao ◽  
Mengyu Li ◽  
Ruxin Gao
Keyword(s):  
Periodic Solution ◽  
Optimization Problem ◽  
Continuation Method ◽  
Problem Formulation ◽  
Correlation Equation ◽  
Jeffcott Rotor ◽  
Optimization Formulation ◽  
Bifurcation Detection ◽  
Tuned Vibration Absorber ◽  
Optimization Problem Formulation

A continuation method for bifurcation tracking is presented based on the proposed optimization problem formulation which is designed to locate the bifurcation periodic solution. The bifurcation detection problem is formulated as a constrained optimization problem. The nonlinear constraints of the optimization problem are imposed on the shooting function and bifurcation conditions derived from the Floquet theory whereas the objective function associated with the pseudo-arclength correlation equation is devised to solution continuation. The proposed optimization formulation is integrated with the prediction–correction strategy to achieve bifurcation tracking. Two numerical examples about the Jeffcott rotor and the nonlinear tuned vibration absorber are illustrated to validate the effectiveness of the proposed methodology. Numerical results have demonstrated that the proposed method offers a convenient scheme to follow bifurcation periodic solution.

scholarly journals Internet shopping optimization problem

2010 ◽  
Vol 20 (2) ◽  
pp. 385-390 ◽  
Author(s):  
JACEK B£A ZÿEWICZ ◽  
Mikhail Kovalyov ◽  
Jędrzej Musiał ◽  
Andrzej Urbanski ◽  
Adam Wojciechowski
Keyword(s):  
Polynomial Time ◽  
Optimization Problem ◽  
Partial Solution ◽  
The Internet ◽  
Internet Shopping ◽  
Single Product ◽  
Polynomial Time Algorithms ◽  
Special Cases ◽  
Multiple Item ◽  
Np Hardness

Internet shopping optimization problemA high number of Internet shops makes it difficult for a customer to review manually all the available offers and select optimal outlets for shopping. A partial solution to the problem is brought by price comparators which produce price rankings from collected offers. However, their possibilities are limited to a comparison of offers for a single product requested by the customer. The issue we investigate in this paper is a multiple-item multiple-shop optimization problem, in which total expenses of a customer to buy a given set of items should be minimized over all available offers. In this paper, the Internet Shopping Optimization Problem (ISOP) is defined in a formal way and a proof of its strong NP-hardness is provided. We also describe polynomial time algorithms for special cases of the problem.

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