The average temperature of the dual region in T0, \(T_{alumn}\), is, therefore, then taken as the valid _Reflected Apparent Temperature_ of _object_ O.

\[T_{refl}=T_{alumn} \tag{1}\]

### Step 2: Real Temperature of a Piece of Electrical Tape near the Object O

Since the emissivity of electrical tape is known (\(\epsilon_{tape}=0.95\)), its real temperature can be obtained by means of Equation (2), in which \(T_{tape\_ap}\) represents the temperature measured by the thermal camera. \(T_{tape\_ap}\) is again calculated after segmenting the area corresponding to the tape in CO. In this case, a simple colour segmentation algorithm provides the solution. The closest segment to the object O is delimited in CO, and the average temperature corresponding to the dual region in TO is taken as the real temperature of the electrical tape. \[T_{tape\_real}=\left(\frac{T_{tape\_ap}^{4}-\left(1-\epsilon_{tape}\right)T_{ ref}^{4}}{\epsilon_{tape}}\right)^{\frac{1}{2}} \tag{2}\]

### Step 3: Emissivity of Object O

The emissivity of the _object_ O is obtained from Equation (3). In this case, it is necessary to measure the temperature provided by the thermal camera in the proximity of the electrical tape. This can be performed by exploring the temperature of a narrow ring around the tape region detected previously in Step 2. The average temperature in this ring is again defined as the apparent temperature of the region near the object and the tape, \(T_{nearby\_object\_ap}\). \[\varepsilon_{object}=\frac{T_{nearby\_object\_ap}^{4}-T_{refl}^{4}}{T_{ tape\_real}^{4}-T_{refl}^{4}} \tag{3}\]

### Step 4: Real Temperature of Object \(O\)

Since it is assumed that the region that covers the complete _object_ O in TO has been calculated beforehand, the average apparent temperature of the object, \(T_{object\_ap}\), is easily obtained. Equation (4) provides the value of the final real temperature of _object_ O.

\[T_{object\_r}=\left[\frac{T_{object\_ap}^{4}-\left[\left(1-\varepsilon_{ object}\right)\cdot T_{refl}^{4}\right]}{\varepsilon_{object}}\right]^{1/4} \tag{4}\]

## 5 Obtaining Transmittances with Real Temperatures

As an application of our method, the corrected temperatures are eventually used to empirically estimate the transmittance (U-value) of the objects on walls (such as door frames, window frames and wall areas). As will be shown in Section 6.4, the experimentation regarding this approach has been conducted under the recommended premises (following ISO 9869:2014, 2018, [20]) of large and stable indoor-outdoor temperature gradients, and without heating and cooling systems. It is possible to classify the experimental U-value assessment methods into methods that do and do not employ the heat flux measurement. With regard to the latter method, the temperature-based methods shown in [21] utilise both the indoor surface temperature and the indoor and outdoor ambient temperature in order to calculate the U-value of the walls. As it is considered that the real temperature is attained by using infrared cameras, it is assumed that this can be included as a new thermography-based method that is extended to the 3D dimension. A literature review on infrared thermography (IRT) based methods was performed by the authors of [22], who stated that infrared thermography-based methods are rapid and reliable under certain specific conditions but that the technique must continue to be refined. Many different approaches and formulas with which to calculate the U-value in this context have been published. The formulation appertaining to Jankovic al. [23] has been employed herein, as follows. The transmittance of an object is defined as the inverse function of the thermal resistance of the object (Equation (5)), which is decomposed into convective and radiative components.