1. A stereoscopic image depth manipulating apparatus comprising: a histogram analyzing unit acquiring a depth distribution chart by performing histogram analysis of a disparity map corresponding to an input image; a Gaussian mixture model (GMM) fitting unit acquiring multiple depth layers by performing GMM fitting of the depth distribution chart; a disparity adjusting unit adjusting at least one of a position and a volume of at least one of the multiple depth layers and calculating a disparity mapping function on which a result of the adjustment is reflected in response to a user request; and a disparity map recalculating unit calculating a new disparity map by optimizing the disparity mapping function, which is calculated by the disparity adjusting unit, wherein the disparity adjusting unit calculates a disparity mapping function d i ′ defined by the following equation in a case where a user selects one of the multiple depth layers and adjusts the volume of the selected depth layer, d i ′ = 1 l ⁢ ∑ j = 1 l ⁢ ⁢ [ d i - { ( d i - μ i ) - ( d i - μ i ) · v j } · ω j ] ω j = π j · G j ⁡ ( d i ) ∑ k = 1 l ⁢ ⁢ π k · G k ⁡ ( d i ) , and here, d i ′ represents a volume-adjusted disparity mapping function, d i represents a disparity mapping function before adjustment, l represents the number of depth layers, μ j represents an average of the j-th Gaussian distribution chart, v j represents a volume value of the j-th depth layer adjusted by the user, G represents a Gaussian function configuring the GMM, and n represents a Gaussian mixture weighting factor.