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@@ -42,10 +42,10 @@ where $\alpha \left( x \right) = 1 - \exp ( - x )$ , and $\delta _ { k } = t _ {
 
 # 3.2 Pre-trained Models and Zero-shot Segmentation of Images
 
-Most semantic segmentation models pre-define a closed set of labels, and cannot flexibly change the segmentation categories or boundaries without supervised training. In contrast, zero-shot semantic segmentation predicts target regions given open-set queries. Li et al. [44] proposes LSeg, a model to feature field f and the pretrained text encoder f . Specifically, probability of a label l of a point x in    2    2Rperform zero-shot semantic segmentation by aligning pixel-level features and a text query feature. 182 the 3D space, p(l x), are predicted by dot product of the 3D feature f (x) and text label feature fq(l)        = Lp + Lf , Lp = C (r)  C(r)  2 , Lf = F(r)  fimg(I, r)  1 , (4)4LSeg employs an image feature encoder with the DPT architecture [71] and a CLIP-based text label 183 followed by softmax: 5stency. In addition, importantly for user-friendly interactive editing, w52R 2Rfeature encoder [69], trained via large-scale language-image contrastive learning. The probability of a text label $l$ 4given a pixel $r$ in an image $I$ , $\mathbf { p } ( l | I , r )$ T 4, is then calculated via dot product of pixel-level image feature ${ \bf f } _ { \mathrm { i m g } } ( I , r )$ p(l|x) = Pand queried text feature ${ \bf f } _ { \mathrm { q } } ( l )$ q  T . followed by a softmax:
+Most semantic segmentation models pre-define a closed set of labels, and cannot flexibly change the segmentation categories or boundaries without supervised training. In contrast, zero-shot semantic segmentation predicts target regions given open-set queries. Li et al. [44] proposes LSeg, a model to feature field f and the pretrained text encoder f . Specifically, probability of a label l of a point x in    2    2Rperform zero-shot semantic segmentation by aligning pixel-level features and a text query feature. 182 the 3D space, p(l x), are predicted by dot product of the 3D feature f (x) and text label feature fq(l)        = Lp + Lf , Lp = C (r)  C(r)  2 , Lf = F(r)  fimg(I, r)  1 , (4)4LSeg employs an image feature encoder with the DPT architecture [71] and a CLIP-based text label 183 followed by softmax: 5stency. In addition, importantly for user-friendly interactive editing, w52R 2Rfeature encoder [69], trained via large-scale language-image contrastive learning. The probability of a text label $l$ 4given a pixel $r$ in an image $I$ , $\mathbf { p } ( l | I , r )$ T 4, is then calculated via dot product of pixel-level image feature ${ \bf f } _ { \mathrm { i m g } } ( I , r )$ p(l|x) = Pand queried text feature ${ \bf f } _ { \mathrm { q } } ( l )$ q  T . followed by a softmax:
 
 ![](images/01c5d617234d256546d0bd2a253fa5222d00322fa46decdbdcc409fa1bb32e21.jpg)  
-as distillation from 2D teacher network to 3D student 4122      k  k+1  k            ˆ                 214 breaks 3D consistency. In addition, importantly f214 breaks 3D consistency. In addition, importantly for usemize f through SGD on minimizing the difference between rendered features F (r) andLp = X  Cˆ (r)  C(r)  , Lf = X  Fˆ(r)  fimg(I, r)  , (4)iginal NeRF [46] for the training objective and the volume rendering strategy. Inps://huggingface.co/sentence-transformers/clip-ViT-B-32-multilingual-v1Figure 1: Left: A Distilled Feature Field (DFF) maps a coordinate x and a viewing direction d to ll this mode 124    work via ther2Rs Fˆ (r) anddensity $\sigma$ eural Perceptual Fields (NePeRF).    els and ground-truth pixels of real images.             nconsistent supervision with noise could harm reconstruction quality of geometry, although the                  lume rendering trick. We call this model distilled feature field (DFF).r2Re teacher’s outputs f (I, r). For volume rendering, we use two 4184         , color c, and feature f . It is trained by minimizing the difference between rendered features sformers/clip-ViT-B-32-multilingual-v1178 effect seems negligible in preliminary experiments.            d at any 3D point without limiting resolution, so naturally used tog41 It is an interesting direction to introduce view de1 It is an interesting direction to introduce view dependehe original NeRF [46] for the training objective and the volume rendering strategy. Inume rendering with coarse-and-fine hierarchical sampling as well as the original185 and feature loss Lf , in total, L:and features as predicted by a pre-trained image feature encoder, as well as the rendered color and 3t is an interesting direction to introduce view dependency to the segmentation for discriminating view-dependent query like referring expressions (e.g., “the chdependent query like referring expressions (e.g., “the chair lef the photometric loss, we add a new objective for minimizing the difference betweenˆ 4          pLf , in total, L:     2ground-truth pixel color. Right: At test time, we may decompose and edit 3D space via selecting and 4 179 4.2 Query-based Decomposition and Editingdent query like referring expressions (e.g., “the chair left to the table”      2020, Liu et      img      or volume rendering with coarse-and-fine hierarchical sampling as well as the originalX  ˆ  2 X  ˆ L = Lp + Lf , Lp manipulating different 3D regions with a variety of queries.
+as distillation from 2D teacher network to 3D student 4122      k  k+1  k            ˆ                 214 breaks 3D consistency. In addition, importantly f214 breaks 3D consistency. In addition, importantly for usemize f through SGD on minimizing the difference between rendered features F (r) andLp = X  Cˆ (r)  C(r)  , Lf = X  Fˆ(r)  fimg(I, r)  , (4)iginal NeRF [46] for the training objective and the volume rendering strategy. Inps://huggingface.co/sentence-transformers/clip-ViT-B-32-multilingual-v1Figure 1: Left: A Distilled Feature Field (DFF) maps a coordinate x and a viewing direction d to ll this mode 124    work via ther2Rs Fˆ (r) anddensity $\sigma$ eural Perceptual Fields (NePeRF).    els and ground-truth pixels of real images.             nconsistent supervision with noise could harm reconstruction quality of geometry, although the                  lume rendering trick. We call this model distilled feature field (DFF).r2Re teacher’s outputs f (I, r). For volume rendering, we use two 4184         , color c, and feature f . It is trained by minimizing the difference between rendered features sformers/clip-ViT-B-32-multilingual-v1178 effect seems negligible in preliminary experiments.            d at any 3D point without limiting resolution, so naturally used tog41 It is an interesting direction to introduce view de1 It is an interesting direction to introduce view dependehe original NeRF [46] for the training objective and the volume rendering strategy. Inume rendering with coarse-and-fine hierarchical sampling as well as the original185 and feature loss Lf , in total, L:and features as predicted by a pre-trained image feature encoder, as well as the rendered color and 3t is an interesting direction to introduce view dependency to the segmentation for discriminating view-dependent query like referring expressions (e.g., “the chdependent query like referring expressions (e.g., “the chair lef the photometric loss, we add a new objective for minimizing the difference betweenˆ 4          pLf , in total, L:     2ground-truth pixel color. Right: At test time, we may decompose and edit 3D space via selecting and 4 179 4.2 Query-based Decomposition and Editingdent query like referring expressions (e.g., “the chair left to the table”      2020, Liu et      img      or volume rendering with coarse-and-fine hierarchical sampling as well as the originalX  ˆ  2 X  ˆ L = Lp + Lf , Lp manipulating different 3D regions with a variety of queries.
 
 $$
 { \bf p } ( l | I , r ) = \frac { \exp ( { \bf f } _ { \mathrm { i m g } } ( I , r ) { \bf f } _ { \mathrm { q } } ( l ) ^ { \mathrm { T } } ) } { \sum _ { l ^ { \prime } \in \mathcal { L } } \exp ( { \bf f } _ { \mathrm { i m g } } ( I , r ) { \bf f } _ { \mathrm { q } } ( l ^ { \prime } ) ^ { \mathrm { T } } ) } ,