Previous |  Up |  Next


Young measures; computer vision equations
In this paper we construct a minimizing sequence for the problem (1). In particular, we show that for any subsolution of the Hamilton-Jacobi equation $(\ast )$ there exists a minimizing sequence weakly convergent to this subsolution. The variational problem (1) arises from the theory of computer vision equations.
[DA] Adams R.A.: Sobolev spaces. Academic Press New York (1975). MR 0450957 | Zbl 0314.46030
[BA] Ball J.M.: A version of the fundamental theorem for Young measures. Lecture Notes in Physics, Springer Verlag 344 (1988), 207-215. MR 1036070
[BL] Berliochi H., Lasry J.M.: Intégrandes normales et mesures parametrées en calcul des variations. (1973), 101 Bull. Soc. Math. France. MR 0344980
[BCK1] Brooks M.J., Chojnacki W., Kozera R.: Shading without shape. Quarterly of Appl. Math., in press. MR 1146621 | Zbl 0763.35103
[BCK2] Brooks M.J., Chojnacki W., Kozera R.: Circularly-symmetric eikonal equations and non-uniqueness in computer vision. J. Math. Analysis and Appl., in press. Zbl 0799.35036
[BR] Anna R. Bruss: The eikonal equation: some results applicable to computer vision. J. Math. Phys. (1982), 23(5) 890-896. MR 0655907
[CZ1] Chabrowski J., Zhang K.: On shape from shading problem. Functional Analysis, Approximation Theory and Numerical Analysis, to appear in: Volume 1 dedicated to S. Banach, S. Ulam and A. Ostrowski, World Scientific Publishing, Singapore. MR 1298653 | Zbl 0878.35026
[CZ2] Chabrowski J., Zhang K.: On variational approach to photometric stereo. Ann. de l'Institut H. Poincaré, Analyse non linéaire, in press. Zbl 0821.49027
[DA] Dacorogna B.: Direct methods in the calculus of variations. Applied Mathematical Sciences 78 Springer Verlag, Berlin - Heidelberg (1989). MR 0990890 | Zbl 0703.49001
[DS] Deift P., Sylvester J.: Some remarks on the shape-from-shading problem in computer vision. J. Math. Anal. Appl. (1982), 84(1) 235-248. MR 0639534
[ET] Ekeland I., Temam R.: Analyse convexe et problèmes variationnels. Dunod Paris (1974). MR 0463993 | Zbl 0281.49001
[EV] Lawrence C. Evans: Weak convergence methods for nonlinear partial differential equations. CBMS Regional Conference Series in Mathematics (74) Amer. Math. Soc. MR 1034481
[KG] Kohn R.V., Strang G.: Optimal design and relaxation of variational problems, I. (1986), 39 Comm. Pure and Applied Math. 113-137. MR 0820342 | Zbl 0609.49008
[KO] Kozera R.: Existence and uniqueness in photometric stereo. Applied Mathematics and Computation (1991), 44(1) 1-103. MR 1110435 | Zbl 0732.53005
[TA] Tartar L.: Compensated compactness. Heriot-Watt Symposium (1978), 4.
Partner of
EuDML logo