1. A quantitative analysis method for estimating energy distributions, comprising steps of: obtaining an energy reading vector X=(x L ,x M ) of a corresponding point pair in an long-wave Infra-red (LIR) image and a medium Infra-red (MIR) image respectively based on an equation (I): [ x L x M ] = [ L H L N M H M N ] ⁡ [ k H k N ] , wherein (L N , M N ) respectively represents the LIR and MIR energy emitted from an unit volume of normal temperature tissue, (L H , M H ) represents the LIR and MIR energy emitted from an unit volume of a high temperature tissue from an unit volume, and k H and k N are two effective volumes of the high temperature tissue and the normal temperature tissue respectively; transforming the equation (I) into an equation (II), by letting L H =A H cos θ, M H =A H sin θ, L N =A N cos φ, M N =A N cos φ: [ x L x M ⁢ ] = [ cos ⁢ ⁢ θ cos ⁢ ⁢ ϕ sin ⁢ ⁢ θ sin ⁢ ⁢ ϕ ] ⁡ [ q H q N ] , wherein q H =A H k H , q N =A N k N , and considering q H and q N as quantities approximately equivalent to the energies of the attenuated LIR and MIR photons originated from the high temperature tissue and the normal temperature tissue respectively, wherein θ and φ are respectively the parameters of the high temperature and the normal temperature of the body region; and establishing a cost function, ƒ, for the quantitative analysis: C and D are smoothness constraints, q N 0 represents an initial state of the q N , and λ is the Lagrange multiplier.