2.1 Design freedom and brand recognition

Several studies have considered the importance of design freedom from the perspective of organizational innovation capability, with a consensus that there is an optimal amount of deviation from previous designs (Hekkert, Snelders & Wieringen Reference Hekkert, Snelders and Wieringen2003; Person et al. Reference Person, Schoormans, Snelders and Karjalainen2008). Customers expect novelty in new product offerings (Martindale Reference Martindale1990), yet such novelty must be bounded (Berlyne Reference Berlyne1971). Companies that follow a ‘design-driven’ approach toward balancing this tradeoff via strategic design decisions have been shown empirically to capture larger market shares (Person et al. Reference Person, Schoormans, Snelders and Karjalainen2008).

The effect of brand recognition on customer preferences has been studied in depth for new product offerings (Aaker & Keller Reference Aaker and Keller1990). General conclusions from these studies are that brands are comprised of highly complex associations between within-brand products and features (Milburn & Childs Reference Milburn and Childs2001; Ranawat, Tuteja & Höltta-Otto Reference Ranawat, Tuteja and Höltta-Otto2012), as well as related people, places, and out-of-brand products (Keller Reference Keller2003). Particularly because automobiles fall under the category of ‘durables,’ namely, products where lifecycle use is important to the customer, brand recognition plays a very important role (Zeithaml Reference Zeithaml1988). These conclusions are aligned with observations in the automotive sector, where brand has been shown to be one of the foremost contributors to customer preference (Mannering et al. Reference Mannering, Winston, Griliches and Schmalensee1991; Motors 2014).

The current study builds on recent results showing that the front fascia or ‘face’ of the vehicle – the view looking directly at the front of the vehicle – is most closely associated with vehicle brand (Ranscombe et al. Reference Ranscombe, Hicks, Mullineux and Singh2012). Moreover, anecdotal evidence from experienced sources within the industry supports this notion (Manoogian II Reference Manoogian2013). Accordingly, all stimuli used in this study consider the face view of vehicle designs.

2.2 Brand-conscious customers

Brand-conscious customers, able to correctly identify brand from unbranded vehicles, are used for filtering the data collected in the study. These brand-conscious customers are filtered, because data from customers unable to identify brand add noise to the construction of predictive models for brand recognition. Moreover, appealing to brand-conscious customers has been found to be important for premium brands such as those considered in this study (Aaker Reference Aaker2009).

Figure 1. Example images shown to customers in the 2D representation portion of the experiment. These images were used to assess styling attribute values, as well as brand recognition. The images remained static (were not morphed by customers) during the experiment and did not contain brand logos.

To identify brand-conscious customers, we filter out customers not able to correctly identify brands above a given threshold for designs that already exist in the market (see below for filtering criteria). Recent literature in crowdsourcing research has shown that data from ‘experts’ within a crowd, in this case ‘brand-conscious customers’ within a crowd, may be aggregated to obtain an accurate ‘crowd consensus vote’ using simple algorithms such as majority vote (Sheng, Provost & Ipeirotis Reference Sheng, Provost and Ipeirotis2008; Sheshadri & Lease Reference Sheshadri and Lease2013). However, if such filtering on the ‘experts’ in the crowd is not done, simple algorithms to aggregate customer input may result in heavily biased crowd-level evaluations (Burnap et al. Reference Burnap, Ren, Gerth, Papazoglou, Gonzalez and Papalambros2015b ). In our current case, this may skew estimates of design freedom when trading off brand recognition. Such filtering of customer data to guide the design process has been similarly explored by using customers to interactively guide the creative aspect of early-stage design (Crilly, Moultrie & Clarkson Reference Crilly, Moultrie and Clarkson2004; Ind & Watt Reference Ind and Watt2006).

2.3 Design representation

Design representation refers to the method that a design artifact is encoded by either a computer or a customer during one of many steps in the design process (Chandrasegaran et al. Reference Chandrasegaran, Ramani, Sriram, Horváth, Bernard, Harik and Gao2013). We make a distinction between the two as it has been shown that computer representations and human representations may be entirely different, resulting in the need to construct models and conduct experiments in the appropriate space (Tversky & Gati Reference Tversky and Gati1978; Tversky & Hutchinson Reference Tversky and Hutchinson1986). Moreover, we consider three different forms of design representation: 2D and 3D model geometries; parametric and nonparametric geometries; and as a function of styling attributes and geometric variables.

2.3.1 2D and 3D representations

Recent studies have shown that brand recognition is dependent on the fidelity of the design representation (Ranscombe et al. Reference Ranscombe, Hicks, Mullineux and Singh2012; Rasoulifar, Prudhomme & Eckert Reference Rasoulifar, Prudhomme and Eckert2015). Informally, there is a level of realism to the design that must be achieved for customers to correctly identify vehicle brand (Orbay, Fu & Kara Reference Orbay, Fu and Kara2015). We build on this notion by representing vehicle designs using the highest fidelity representation possible whether a 2D image or a 3D high polygon mesh, as shown in Figures 1 and 2, respectively.

Figure 2. Example images shown to customers in the 2D representation portion of the experiment. These images were used to assess styling attribute values, as well as brand recognition. The images remained static (were not morphed by customers) during the experiment and did not contain brand logos.

Studies have also shown differences between 2D and 3D design representations regardless of fidelity. In particular, customer preferences assessed through conjoint analysis have been found to be inconsistent when contrasting the type of design representation (Reid, MacDonald & Du Reference Reid, MacDonald and Du2013; Bao et al. Reference Bao, El Ferik, Shaukat and Yang2014; Toh & Miller Reference Toh and Miller2014). The area of assessing the level of fidelity or abstraction to a given threshold for a customer’s perception is still an active area of research, including both 2D and 3D representations.

2.4 Quantitative models of product styling

Previous research in quantitative modeling of styling and aesthetics has often come from the marketing community, where conjoint analysis has proven valuable (Green, Carroll & Goldberg Reference Green, Carroll and Goldberg1981). This modeling technique takes a number of variables representing the design’s form as input and elicits customer preferences across a set of discrete points within the design space.

The design community has similarly used conjoint analysis to model styling form in efforts to optimize customer preferences in decision-based design (Hazelrigg Reference Hazelrigg1998; Papalambros Reference Papalambros2002; Chen, Hoyle & Wassenaar Reference Chen, Hoyle and Wassenaar2013). Relevant examples of such applications include 2D vehicle side view silhouettes (Orsborn et al. Reference Orsborn, Cagan and Boatwright2009; Reid et al. Reference Reid, Gonzalez and Papalambros2010) and 2D vehicle faces (Petiot & Dagher Reference Petiot and Dagher2010). Recently, 3D vehicle studies such as perceived safety (Ren et al. Reference Ren, Burnap and Papalambros2013) and vehicle interiors (Poirson et al. Reference Poirson, Petiot, Boivin and Blumenthal2013), as well as virtual reality studies (Tovares et al. Reference Tovares, Boatwright and Cagan2014) have been investigated. Some applications have used nonlinear conjoint models such as explicit feature mappings (Fuge, Stroud & Agogino Reference Fuge, Stroud and Agogino2013) and implicit feature mappings (Ren et al. Reference Ren, Burnap and Papalambros2013). Additional 3D extensions include the use of hierarchical geometric representations that may be used for salient feature extraction (Orbay et al. Reference Orbay, Fu and Kara2015).

Figure 3. Dependencies between design freedom and brand recognition, design attributes, and design variables. Note that while design freedom and brand recognition are explicit linear functions of design attributes, design attributes are nonlinear functions of geometric design variables implicit in the customer perceptions of vehicles. In other words, we know the function for the top mapping, while we do not know the function for the bottom mapping. On the right-hand side, we denote the functional form of the associated dependencies.

3.1 L1 multinomial logit for brand recognition

We define brand recognition as a linear combination of design attributes, in which the attributes maximally discriminate between brands. To determine the linear coefficients to predict brand, we assume a multinomial logistic regression functional form, conditioned only on brand-conscious customers and regularized using the L1-norm, as given in Eq. (1).

(1) $$\begin{eqnarray}\displaystyle f_{b}^{BR}(\mathbf{a})=\frac{e^{\mathbf{w}_{b}^{T}\mathbf{a}}}{\mathop{\sum }_{b=1}^{B}e^{\mathbf{w}_{b}^{T}\mathbf{a}}}+|\mathbf{w}_{b}|_{1}. & & \displaystyle\end{eqnarray}$$

To train the coefficients $\mathbf{w}_{b}$ of this model, we use a quasi-Newton optimization algorithm (l-BFGS) to maximize the penalized multinomial likelihood (Papalambros & Wilde Reference Papalambros and Wilde2000). Note that we use here the notation for coefficients from the machine learning literature; these coefficients are also often denoted with the symbols $\unicode[STIX]{x1D6FD}$ in marketing and $\unicode[STIX]{x1D703}$ in statistics. The data are conditioned using a hard threshold, where a brand-conscious customer must achieve greater than $T$ percentage correct recognition of brands across a set of existing designs.

3.2 Design freedom distance metric

Design freedom is the leeway designers have to generate conceptual designs while accounting for many implicit and explicit constraints (Hartley Reference Hartley1996). To capture this leeway, we adopt the information processing flow in Crilly et al. (Reference Crilly, Moultrie and Clarkson2004) by assuming that the communication from designer to customer is conveyed through information of multiple modes – in our case a vector of design attributes and vector of geometric values representing the design artifact.

With this design representation of multiple modes, we define design freedom as a distance from existing designs to a new conceptual design both across design attributes and across geometric variables. This design freedom distance is mathematically captured using a distance metrics; yet while various metrics have been previously used for engineering specifications (Simpson et al. Reference Simpson, Rosen, Allen and Mistree1998), representations such as abstract knowledge databases (Chandrasegaran et al. Reference Chandrasegaran, Ramani, Sriram, Horváth, Bernard, Harik and Gao2013), and text (Fu et al. Reference Fu, Chan, Cagan, Kotovsky, Schunn and Wood2013), these metrics do not accommodate various stakeholder inputs as specifically needed in the current study.

We thus propose a distance metric between two designs $\unicode[STIX]{x1D6FC}$ and $\unicode[STIX]{x1D6FD}$ for brand $b$ as given in Eq. (2). This metric is used to assign a scalar value that captures both geometric and perceptual styling differences between designs.

(2) $$\begin{eqnarray}\displaystyle \Vert f_{b}^{DF,\unicode[STIX]{x1D6FC}}-f_{b}^{DF,\unicode[STIX]{x1D6FD}}\Vert & = & \displaystyle \mathop{\sum }_{m=1}^{M}\mathbb{I}_{w_{b,m\neq }0}\left[\vphantom{\mathop{\sum }_{n=1}^{N}}\unicode[STIX]{x1D706}_{1}(a_{m}^{(\unicode[STIX]{x1D6FC})}-a_{m}^{(\unicode[STIX]{x1D6FD})})^{2}\right.\nonumber\\ \displaystyle & & \displaystyle +\,\left.\unicode[STIX]{x1D706}_{2}\mathop{\sum }_{n=1}^{N}r_{b,nm}(x_{n}^{(\unicode[STIX]{x1D6FC})}-x_{n}^{(\unicode[STIX]{x1D6FD})})^{2}\right]\end{eqnarray}$$

where,

$$\begin{eqnarray}\displaystyle & & \displaystyle a_{m}=\text{ design attributes measured using 2D representation}\nonumber\\ \displaystyle & & \displaystyle x_{n}=\text{ geometric design variables common to both 2D and 3D representations}\nonumber\\ \displaystyle & & \displaystyle \unicode[STIX]{x1D706}_{1}=\text{ importance/normalizing operator of design attributes}\nonumber\\ \displaystyle & & \displaystyle \unicode[STIX]{x1D706}_{2}=\text{ importance/normalizing operator of geometric design variables}\nonumber\\ \displaystyle & & \displaystyle \mathbb{I}_{w_{b,m\neq }0}=\text{ indicator function if attribute }m\text{ is important for brand }b\nonumber\\ \displaystyle & & \displaystyle r_{b,nm}=\text{ sensitivity of attribute }m\text{ to variable }n\text{ for brand }b.\nonumber\end{eqnarray}$$

This distance metric captures stakeholder considerations to the overall design freedom in two ways: First, design freedom implicit in the mind of the customer is captured using $r_{(b,nm)}$ and $\mathbb{I}_{w_{b,m\neq }0}$ , both of which are assessed using the customer crowd. Informally, these values capture the notion that differences between two designs exist with both geometric and perceptual representations in the mind of the customer.

Second, design freedom explicit from stakeholders within the producing organization is captured using $\unicode[STIX]{x1D706}_{1}$ and $\unicode[STIX]{x1D706}_{2}$ , which may represent, say, relative influences of the marketing and engineering departments, respectively. Informally, we use these operators to tune how important it is to maintain an attribute like ‘aggressiveness’ for a marketing campaign, or a certain geometric shape for vehicle aerodynamics. Accordingly, these operators are specific to the brand being considered.

Using this distance metric, overall design freedom is assessed as the distance from the current design in Model Year 2014 (MY2014) to a proposed design $(\mathbf{x}^{\prime },\mathbf{a}^{\prime })$ . Denoting the current design $(\mathbf{x}^{0},\mathbf{a}^{0})$ , design freedom for the proposed design is given by Eq. (3) using vector notation for brevity.

(3) $$\begin{eqnarray}\displaystyle f_{b}^{DF}(\mathbf{x}^{\prime },\mathbf{a}^{\prime }) & = & \displaystyle \Vert f_{b}^{DF}(\mathbf{x}^{\prime },\mathbf{a}^{\prime })-f_{b}^{DF}(\mathbf{x}^{0},\mathbf{a}^{0})\Vert \nonumber\\ \displaystyle & = & \displaystyle \unicode[STIX]{x1D706}_{1}(\mathbf{a}^{\prime }-\mathbf{a}^{0})^{T}\text{diag}[\mathbb{I}_{\mathbf{w}_{b\neq }0}](\mathbf{a}^{\prime }-\mathbf{a}^{0})\nonumber\\ \displaystyle & & \displaystyle +\,\unicode[STIX]{x1D706}_{2}(\mathbf{x}^{\prime }-\mathbf{x}^{0})^{T}\text{diag}[\mathbf{R}\mathbb{I}_{\mathbf{w}_{b\neq }0}](\mathbf{x}^{\prime }-\mathbf{x}^{0})\end{eqnarray}$$

where,

$$\begin{eqnarray}\displaystyle & & \displaystyle \mathbb{I}_{\mathbf{w}_{b\neq }0}=Mx1\text{ vector of indicator functions for brand }b\nonumber\\ \displaystyle & & \displaystyle \mathbf{R}=NxM\text{ matrix of attribute {-} variable sensitivities}\nonumber\\ \displaystyle & & \displaystyle \text{diag}[\cdot ]=\text{ operator to transform vectors to diagonal matrices}.\nonumber\end{eqnarray}$$

To calculate the sensitivities of design attributes to design variables $r_{(b,nm)}$ , we conduct a one-sided $t$ -test between the baseline design variable $x_{n}^{0}$ and the morphed $x_{n}^{\prime }$ from customer responses for a given attribute $m$ and brand $b$ . This hypothesis test sets the $r_{(b,nm)}=1$ if the $p$ -value for the $t$ -test is less than 0.05, and $r_{(b,nm)}=0$ otherwise. The values of the indicator function $\mathbb{I}_{w_{b,m\neq }0}$ are calculated by assigning the value 1 to all nonzero elements of the corresponding weight vector described in Section 3.1. This weight vector is already sparse due to L1 regularization, and is thus suited to picking out attributes that most contribute to the brand styling (Ranawat et al. Reference Ranawat, Tuteja and Höltta-Otto2012).

3.3 Crowdsourced Markov chain for design attributes

Our next goal is to develop a method of obtaining the attribute values for each design, for example, ‘this vehicle is 0.7 out of 1.0 for aggressiveness, 0.2 out of 1.0 for distinctiveness,’ and so on. This method is a function that maps a design’s geometric variables $\mathbf{x}$ to the design’s corresponding attributes $\mathbf{a}$ .

Within the design community, this function has conventionally been approximated by explicitly assuming a functional form, such as the linear logit model often used in design utility theory treatments, followed by estimating part-worth coefficients of the assumed model. However, this function is likely highly nonlinear, particularly when dealing with high-dimensional representations required for realistic design stimuli.

Here we take a different approach by assuming that the nonlinear function relating design attributes to design variables is implicitly captured by the responses of brand-conscious customers. By crowdsourcing the attribute values of the designs – asking a crowd of customers to evaluate designs over attributes – we avoid needing to make a priori assumptions regarding this complex nonlinear functional form explicitly. This has advantages as we are capturing a function that may exist in a more expressive function space, allowing complex modeling of nonlinear interactions. Moreover, we avoid the need of explicit mathematical representation of geometric variables, given that realistic 3D vehicle polygon meshes may contain more than 100 000 vertices.

Under this approach, there are several ways to extract attribute values of designs from the evaluations provided by the crowd. We choose to extract these values using only relative comparisons between the set of designs, avoiding the notion of a nonrelative scale, i.e., ‘what would it mean to give a design a 0.4 out of 1.0 ‘aggressive’ score without seeing the entire set of designs, and how could we ensure everyone used the same scale?’

In particular, we ask the crowd to evaluate the attributes of designs as a ranking between just a few designs at a time. Formally, the responses ${r_{c}}_{1}^{C}$ made by customers $c=1\ldots C$ , in which each evaluation is in the form of a partial ranking for a single design attribute. Partial rankings without ties are chosen as more intuitive for human evaluation (Gonzalez & Nelson Reference Gonzalez and Nelson1996).

To obtain attribute values using this set of evaluation responses from the crowd, i.e., to aggregate these partial rankings into numbers for each attribute and for each design, we derive a Markov chain solved using a modified version of PageRank (Brin & Page Reference Brin and Page1998) as given in Eqs (4), (5), and (6). Informally, this Markov chain treats the ranking of all designs for a specific attribute as a set of ‘states,’ for car designs to jump between. Every time a car is ranked above another, that car pair jumps to the higher ranked state. The set of states that correspond to the maximal number of correctly ranked cars is called the ‘stationary distribution.’ Finding this desired final ranking of states requires an iterative optimization procedure.

Figure 4. Diagram of Markov chain used to aggregate customer responses in the form of partial rankings of cars to obtain design attribute values for each brand. Black arrows show nonzero transition probabilities from the raw transition matrix, while red dashed arrows show perturbation probabilities added to ensure a unique stationary distribution.

This iterative procedure is characterized by the Markov chain jumping around different states as shown in Figure 4. This jumping action is governed by a transition probability from one state to another, and in our case those transition probabilities depend on partial rankings. The converged stationary probability distribution of the Markov chain is then used as the value of the attribute. Specifically, we define the attribute value as the probability that the car is ranked higher than other cars, thus the attribute value of a car equals its average percentage of the time that it is ranked higher than other competing cars. Following the jumping analogy, if a car is more likely to be ranked higher than others, then the agent will jump into that state more often.

More formally, the transition probability $P_{ij},i,j=1,\ldots ,N$ from the state representing car $i$ to the state representing car $j$ is defined as the frequency that car $j$ is ranked higher than car $i$ in all partial ranks that contain car $i$ . If the transition probability $P_{ij}$ is large, we define car $j$ as being more likely to have greater relative attribute value than car $i$ . We denote the transition probability matrix as $\mathbf{P}=(P_{ij})$ , hereafter referred to as the raw transition probability matrix. The stationary distribution $\unicode[STIX]{x1D70B}$ of a Markov chain is a distribution vector unchanged after the operation of transition matrix $\mathbf{P}$ , as given in Eq. (4).

(4) $$\begin{eqnarray}\displaystyle \boldsymbol{\unicode[STIX]{x1D70B}}=\boldsymbol{\unicode[STIX]{x1D70B}}\mathbf{P} & & \displaystyle\end{eqnarray}$$

$$\begin{eqnarray}\displaystyle & \boldsymbol{\unicode[STIX]{x1D70B}}=(\unicode[STIX]{x1D70B}_{1},\unicode[STIX]{x1D70B}_{2},\ldots ,\unicode[STIX]{x1D70B}_{N}) & \displaystyle \nonumber\\ \displaystyle & \displaystyle \unicode[STIX]{x1D70B}_{i}\geqslant 0\quad \text{and}\quad \mathop{\sum }_{i=1}^{N}\unicode[STIX]{x1D70B}_{i}=1. & \displaystyle \nonumber\end{eqnarray}$$

Consistent with Markov chain theory, there is no guarantee that the raw transition probability matrix $\mathbf{P}$ will have unique stationary distribution (Ross Reference Ross1996) without some strong assumptions. To achieve uniqueness in the resulting distribution, we make two extensions to convert the raw transition matrix $\mathbf{P}$ to a stochastic, irreducible, and aperiodic matrix (Brin & Page Reference Brin and Page1998).

3.3.1 Extension 1

The rows in $\mathbf{P}$ containing only 0’s are replaced with $\frac{1}{N}\mathbf{e}^{T}$ , where $\mathbf{e}^{T}$ is a column vector consisting of 1’s, and $T$ denotes the transpose operator. This adjustment results in a stochastic matrix denoted by $\mathbf{S}$ as given in Eq. (5).

(5) $$\begin{eqnarray}\displaystyle \mathbf{S}=\mathbf{P}+\mathbf{Q}\left(\frac{1}{N}\mathbf{e}^{T}\right) & & \displaystyle\end{eqnarray}$$

$$\begin{eqnarray}\displaystyle Q_{i}=\left\{\begin{array}{@{}ll@{}}1\quad & \text{if }P_{i}=\mathbf{0}\\ 0\quad & \text{otherwise}.\end{array}\right. & & \displaystyle \nonumber\end{eqnarray}$$

3.3.2 Extension 2

To convert $\mathbf{S}$ into an irreducible and aperiodic matrix $\mathbf{G}$ , we use Eq. (6).

(6) $$\begin{eqnarray}\displaystyle \mathbf{G}=\unicode[STIX]{x1D6FE}\mathbf{S}+(1-\unicode[STIX]{x1D6FE})\frac{1}{N}\mathbf{e}\mathbf{e}^{T} & & \displaystyle\end{eqnarray}$$

where $\unicode[STIX]{x1D6FE}$ is a scalar between 0 and 1 controlling the intensity of the perturbation that ensures uniqueness.

With these extensions, a unique stationary distribution exists for $\mathbf{G}$ . From Eq. (6), the stationary distribution vector $\boldsymbol{\unicode[STIX]{x1D70B}}$ can be obtained by calculating the eigenvectors of $\mathbf{G}$ or by iteratively calculating $\boldsymbol{\unicode[STIX]{x1D70B}}^{(k+1)}=\boldsymbol{\unicode[STIX]{x1D70B}}^{(k)}\mathbf{G},k=1,2,\ldots$ until convergence. To calculate the values of attributes $\mathbf{a}_{b}$ for brand $b$ based on the set of all partial rankings from customer responses ${r_{c}}_{1}^{C}$ , we define the attribute value for car $i$ as $\unicode[STIX]{x1D70B}_{m},m=1,2,\ldots ,M$ .

4.1 Customers

We gathered a total of 315 customers through the crowdsourcing platform Amazon Mechanical Turk. As online crowdsourcing has been empirically shown to be a noisy process, partially due to various motivations of customers (Gerth, Burnap & Papalambros Reference Gerth, Burnap and Papalambros2012; Pilz & Gewald Reference Pilz and Gewald2013; Sheshadri & Lease Reference Sheshadri and Lease2013; Panchal Reference Panchal2015), we filtered out data from customers using two data processing steps to ensure data fidelity.

First, customers that simply ‘clicked through’ the survey were filtered out by requiring their average time on the 2D portion of the site to be greater than 6 s per ranking. Second, a brand recognition accuracy threshold of 30% was chosen to filter out customers who were not ‘brand-conscious’ as justified in Section 2. For reference, the average brand recognition accuracy for the unfiltered crowd was 32.78%. Brand recognition accuracy was treated as a constant variable across the entire survey, and all data were filtered out for a given participant if he or she did not fall above the threshold.

After filtering mechanisms, 139 customers were retained from a total of 315 customers gathered over two experiments, as described in the experimental procedure. In particular, experiments gathered 196 and 119 customers, of which 96 and 43 remained after filtering, respectively.

4.2 Vehicle brands and models

The brands chosen were Audi, BMW, Cadillac, and Lexus ( $B=4$ ), due to their relative similarities over a targeted market segment of luxury vehicles, as well as similarity of product offerings across vehicle classes. For each brand, five models were chosen from MY2014 corresponding to five vehicle classes as given in Table 1.

Table 1. Description of the four vehicle manufacturer brands and five associated vehicle classes used in this study

Figure 5. 2D Images of MY2014 Vehicles with brand emblems removed.

4.3 2D images and 3D morphable vehicle models

Images of the vehicle face were sourced from an online vendor. The face viewpoint has been shown to be more correlated with brand recognition than side view or rear vehicle view (Ranscombe et al. Reference Ranscombe, Hicks, Mullineux and Singh2012). Each image consisted of a white vehicle on a white background to minimize confounding interactions from color as shown in Figure 1. Moreover, the brand logo was removed for each vehicle image in order to focus customer responses just on styling as in Orbay et al. (Reference Orbay, Fu and Kara2015). All 2D representations are shown in Figure 5.

Four morphable 3D models, one for each brand, were created as shown in Figure 2. Morphing was precomputed offline using Laplacian deformation and volumetric-based mesh deformation techniques (Botsch & Sorkine Reference Botsch and Sorkine2008). The models were then imported into the web-based survey using the browser-based WebGL renderer, allowing real-time and realistic deformation via client-side graphics processing unit interpolation.

4.4 Design attributes

As discussed above, design attributes link brand recognition with design freedom. We selected ten design attributes given in Table 2 based on input from actual design teams in the automotive industry (Motors 2014).

Table 2. Description of the four vehicle manufacturer brands and five associated vehicle classes used in this study

4.5 Experimental procedure

We conducted two experiments: Experiment 1 gathered attribute values and brand recognition accuracies via partial rankings of 2D images of MY2014 baseline designs. This was followed by generation of new morphed concept designs using a 3D morphable model. Experiment 2 similarly gathered attribute values and brand recognition accuracies, except this time using 2D images of both the MY2014 baseline designs mixed with 2D images of the 3D morphed concept designs from Experiment 1. The overall procedure is given in Figure 6, and was as follows.

Figure 6. Overview of the experimental procedure for both Experiment 1 and Experiment 2. Experiment 1 asked participants to give partial rankings of current MY2014 baseline designs for a given design attribute, followed by asking which brand each of the images corresponded to. Participants were then asked to morph a 3D design to create new concept designs given the same design attribute. Experiment 2 asked a different set of participants to give partial rankings of current MY2014 baseline designs mixed with images of the morphed concept designs from Experiment 1. Similarly, participants were then asked which each brand the images corresponded to.

4.5.1 Experiment 1

Participants were first directed to an introduction page, where they were given instructions on ranking vehicles according to a semantic differential. This semantic differential consisted of only one of the ten attributes from low to high value or vice versa to act as a counterbalance for ordering biases. Over the entire interactive survey, a participant was always given the same semantic differential to reduce participant burden.

Next, participants were directed to the 2D design ranking page, with the four vehicles in a top row and four outlined placeholders in a bottom row as shown in Figure 7. Instructions on the page were given to drag and drop the four MY2014 baseline designs from the top row to the bottom row using the mouse, including possibility of reordering the partial ranking. Upon clicking the ‘Submit’ button for the partial ranking, participants were then asked to choose the brand of each MY2014 baseline design using a drop-down menu with 34 possible options (e.g., Audi, Volvo, Toyota).

Figure 7. Snapshot of 3D morphing design from online web application.

After participants chose a recognized brand for each of the vehicles, they were allowed to continue to the next partial ranking. After participants completed five partial rankings on the 2D portion of the site, they were directed to the 3D portion of the site for generating new designs. In this portion, each participant was given a randomly chosen 3D model in the midsize vehicle segment from the four brands as shown in Figure 8. Participants were then asked to maximize the same design attribute as their semantic differential from the 2D portion of the site by morphing the 3D design using four sliders. They were able to rotate the 3D vehicle model to assess the gestalt of the face. Upon submitting their chosen 3D design, participants were then directed to a short survey in which they were asked basic demographic information as well as task relevant information.

Figure 8. Snapshot of 3D morphing design from online web application.

4.5.2 Experiment 2

A new set of participants was asked to give partial rankings for a randomly assigned design attribute, but now with both 2D images of MY2014 baseline designs mixed with 2D images of face views of the 3D morphed concept designs from Experiment 1. Recall that this mixture of MY2014 baseline designs and morphed concept designs is necessary to get relative attribute values using the partial ranking Markov chain method derived earlier. A total of 52 possible 2D images was shown to participants, 20 from the original MY2014 baseline designs given in Table 1, and 32 from 3D designs morphed concept designs from Experiment 1.

Figure 9. Diagram of the data flow and methods used in the data analysis of the experiment. As described earlier and shown in Figure 5, Experiment 1 provides the Partial Ranking Markov Chain and L1 Multinomial Regression with data from only MY2014 vehicle designs, thus provided the attribute–variable sensitivities  $\mathbf{R}$ and brand–attribute sensitivities $\mathbb{I}_{(\unicode[STIX]{x1D714}\neq 0)}$ . Experiment 2 provides the Partial Ranking Markov Chain with combined MY2014 and morphed vehicle designs, of which only morphed design attributes and variables are passed on to the Design Freedom Distance Metric. The values of design freedom for each morphed design are then compared with their corresponding brand recognition to obtain the desired slope on a brand-by-brand basis.

4.6 Brand recognition versus design freedom data analysis

We give a diagram in Figure 9 of the data analysis using the methods detailed and developed in Section 3, and list this methods flow here: We aggregated the partial rankings from each brand-conscious participant using the method described earlier to obtain the design attribute values for each new conceptual design. These design attributes were used to build a model of brand recognition. The filtered data included participants from 2D images of both morphed and nonmorphed designs due to the relative values obtained using the partial ranking aggregation method.

Brand recognition was assessed by calculating the number of correct responses to the set of 32 morphed conceptual designs over the total number of times that particular conceptual design showed up in the partial rankings. Design freedom was calculated using the metric described above. The operators $\unicode[STIX]{x1D706}_{1}$ and $\unicode[STIX]{x1D706}_{2}$ are chosen to scale the design freedom by subtracting the mean and dividing the standard deviation of each brand’s design variables and design attributes, respectively, resulting in a normalized design freedom. This operation was chosen on a brand-by-brand basis as this did not change the brand recognition versus design freedom distributions.

Figure 10. Brand recognition versus design freedom for the four vehicle brands in this study over 2D images taken of the conceptual designs generated during the 3D portion of the experiment. Brand recognition accuracy is defined as the percentage of time a brand-conscious customer – a customer who correctly identified more than 30% of the MY2014 baseline vehicle brands – was able to correctly recognize a new morphed design. Note that design freedom values have been normalized within the brand such that the four brands may be meaningfully compared – this operation results in negative values of design freedom though the original values are always nonnegative.