bundle block adjustment with 3d natural cubic splines

[42],Tommaselli and Lugnani(1988) [70], Heikkilä(1991) [32], Kubik(1992) [37], Petsaand Patias(1994) [50], Gülch(1995) [20], Wiman and Axelsson(1996) [76], Chen andShibasaki(1998) [12], Habib(1999) [26], Heuvel(1999) [34], Tommaselli(1999) [71],Vosselman and Veldhuis(1999)[73], Föstner(2000) [17], Smith and Park(2000) [65],Schenk(2002) [58], Tangelder et al.(2003) [68] and Parian and Gruen(2005) [49]. In1988 Mulawa and Mikhail[47] proved the feasibility of linear features for close-rangephotogrammetric applications such as the space intersection, the space resection, relativeorientation and absolute orientation. This was the first step to employ the linearfeature based method in the close-range photogrammetric applications. Mulawa[46]developed linear feature based methods for different sensors. While straight linearfeatures and conic sections can be represented as unique mathematical expressions,free-form lines in nature cannot be described by algebraic equations. Hence Mikhailand Weerawong[44] employed splines and polylines to express free-form lines as analyticalexpressions.Tommaselli and Tozzi[72] proposed that the accuracy of thestraight line parameter should be a sub-pixel with the representation of four degreesof freedom in an infinite line. Many researchers in photogrammetry have describedstraight lines as infinite lines using minimal representation to reduce unknown parameters.The main consideration of straight line expression is singularities. Habibet al.[29] performed the bundle block adjustment using 3D point set lying on controllinear features instead of traditional control points. EOPs were reconstructed hierarchicallyemploying automatic single photo resection (SPR). SPR was implementedby the relationship between image and object space points expressed as EOPs asfollowing equation (2.8).16