Add multiimage and gaussian

app.py

@@ -9,7 +9,6 @@ from typing import *
 import torch
 import numpy as np
 import imageio
-import uuid
 from easydict import EasyDict as edict
 from PIL import Image
 from trellis.pipelines import TrellisImageTo3DPipeline
@@ -24,17 +23,15 @@ os.makedirs(TMP_DIR, exist_ok=True)
 
 def start_session(req: gr.Request):
     user_dir = os.path.join(TMP_DIR, str(req.session_hash))
-    print(f'Creating user directory: {user_dir}')
     os.makedirs(user_dir, exist_ok=True)
     
     
 def end_session(req: gr.Request):
     user_dir = os.path.join(TMP_DIR, str(req.session_hash))
-    print(f'Removing user directory: {user_dir}')
     shutil.rmtree(user_dir)
 
 
-def preprocess_image(image: Image.Image) -> Tuple[str, Image.Image]:
+def preprocess_image(image: Image.Image) -> Image.Image:
     """
     Preprocess the input image.
 
@@ -42,14 +39,28 @@ def preprocess_image(image: Image.Image) -> Tuple[str, Image.Image]:
         image (Image.Image): The input image.
 
     Returns:
-        str: uuid of the trial.
         Image.Image: The preprocessed image.
     """
     processed_image = pipeline.preprocess_image(image)
     return processed_image
 
 
-def pack_state(gs: Gaussian, mesh: MeshExtractResult, trial_id: str) -> dict:
+def preprocess_images(images: List[Tuple[Image.Image, str]]) -> List[Image.Image]:
+    """
+    Preprocess a list of input images.
+    
+    Args:
+        images (List[Tuple[Image.Image, str]]): The input images.
+        
+    Returns:
+        List[Image.Image]: The preprocessed images.
+    """
+    images = [image[0] for image in images]
+    processed_images = [pipeline.preprocess_image(image) for image in images]
+    return processed_images
+
+
+def pack_state(gs: Gaussian, mesh: MeshExtractResult) -> dict:
     return {
         'gaussian': {
             **gs.init_params,
@@ -63,7 +74,6 @@ def pack_state(gs: Gaussian, mesh: MeshExtractResult, trial_id: str) -> dict:
             'vertices': mesh.vertices.cpu().numpy(),
             'faces': mesh.faces.cpu().numpy(),
         },
-        'trial_id': trial_id,
     }
     
     
@@ -87,7 +97,7 @@ def unpack_state(state: dict) -> Tuple[Gaussian, edict, str]:
         faces=torch.tensor(state['mesh']['faces'], device='cuda'),
     )
     
-    return gs, mesh, state['trial_id']
+    return gs, mesh
 
 
 def get_seed(randomize_seed: bool, seed: int) -> int:
@@ -100,11 +110,14 @@ def get_seed(randomize_seed: bool, seed: int) -> int:
 @spaces.GPU
 def image_to_3d(
     image: Image.Image,
+    multiimages: List[Tuple[Image.Image, str]],
+    is_multiimage: bool,
     seed: int,
     ss_guidance_strength: float,
     ss_sampling_steps: int,
     slat_guidance_strength: float,
     slat_sampling_steps: int,
+    multiimage_algo: Literal["multidiffusion", "stochastic"],
     req: gr.Request,
 ) -> Tuple[dict, str]:
     """
@@ -112,43 +125,62 @@ def image_to_3d(
 
     Args:
         image (Image.Image): The input image.
+        multiimages (List[Tuple[Image.Image, str]]): The input images in multi-image mode.
+        is_multiimage (bool): Whether is in multi-image mode.
         seed (int): The random seed.
         ss_guidance_strength (float): The guidance strength for sparse structure generation.
         ss_sampling_steps (int): The number of sampling steps for sparse structure generation.
         slat_guidance_strength (float): The guidance strength for structured latent generation.
         slat_sampling_steps (int): The number of sampling steps for structured latent generation.
+        multiimage_algo (Literal["multidiffusion", "stochastic"]): The algorithm for multi-image generation.
 
     Returns:
         dict: The information of the generated 3D model.
         str: The path to the video of the 3D model.
     """
     user_dir = os.path.join(TMP_DIR, str(req.session_hash))
-    outputs = pipeline.run(
-        image,
-        seed=seed,
-        formats=["gaussian", "mesh"],
-        preprocess_image=False,
-        sparse_structure_sampler_params={
-            "steps": ss_sampling_steps,
-            "cfg_strength": ss_guidance_strength,
-        },
-        slat_sampler_params={
-            "steps": slat_sampling_steps,
-            "cfg_strength": slat_guidance_strength,
-        },
-    )
+    if not is_multiimage:
+        outputs = pipeline.run(
+            image,
+            seed=seed,
+            formats=["gaussian", "mesh"],
+            preprocess_image=False,
+            sparse_structure_sampler_params={
+                "steps": ss_sampling_steps,
+                "cfg_strength": ss_guidance_strength,
+            },
+            slat_sampler_params={
+                "steps": slat_sampling_steps,
+                "cfg_strength": slat_guidance_strength,
+            },
+        )
+    else:
+        outputs = pipeline.run_multi_image(
+            [image[0] for image in multiimages],
+            seed=seed,
+            formats=["gaussian", "mesh"],
+            preprocess_image=False,
+            sparse_structure_sampler_params={
+                "steps": ss_sampling_steps,
+                "cfg_strength": ss_guidance_strength,
+            },
+            slat_sampler_params={
+                "steps": slat_sampling_steps,
+                "cfg_strength": slat_guidance_strength,
+            },
+            mode=multiimage_algo,
+        )
     video = render_utils.render_video(outputs['gaussian'][0], num_frames=120)['color']
     video_geo = render_utils.render_video(outputs['mesh'][0], num_frames=120)['normal']
     video = [np.concatenate([video[i], video_geo[i]], axis=1) for i in range(len(video))]
-    trial_id = uuid.uuid4()
-    video_path = os.path.join(user_dir, f"{trial_id}.mp4")
+    video_path = os.path.join(user_dir, 'sample.mp4')
     imageio.mimsave(video_path, video, fps=15)
-    state = pack_state(outputs['gaussian'][0], outputs['mesh'][0], trial_id)
+    state = pack_state(outputs['gaussian'][0], outputs['mesh'][0])
     torch.cuda.empty_cache()
     return state, video_path
 
 
-@spaces.GPU
+@spaces.GPU(duration=90)
 def extract_glb(
     state: dict,
     mesh_simplify: float,
@@ -167,24 +199,83 @@ def extract_glb(
         str: The path to the extracted GLB file.
     """
     user_dir = os.path.join(TMP_DIR, str(req.session_hash))
-    gs, mesh, trial_id = unpack_state(state)
+    gs, mesh = unpack_state(state)
     glb = postprocessing_utils.to_glb(gs, mesh, simplify=mesh_simplify, texture_size=texture_size, verbose=False)
-    glb_path = os.path.join(user_dir, f"{trial_id}.glb")
+    glb_path = os.path.join(user_dir, 'sample.glb')
     glb.export(glb_path)
     torch.cuda.empty_cache()
     return glb_path, glb_path
 
 
+@spaces.GPU
+def extract_gaussian(state: dict, req: gr.Request) -> Tuple[str, str]:
+    """
+    Extract a Gaussian file from the 3D model.
+
+    Args:
+        state (dict): The state of the generated 3D model.
+
+    Returns:
+        str: The path to the extracted Gaussian file.
+    """
+    user_dir = os.path.join(TMP_DIR, str(req.session_hash))
+    gs, _ = unpack_state(state)
+    gaussian_path = os.path.join(user_dir, 'sample.ply')
+    gs.save_ply(gaussian_path)
+    torch.cuda.empty_cache()
+    return gaussian_path, gaussian_path
+
+
+def prepare_multi_example() -> List[Image.Image]:
+    multi_case = list(set([i.split('_')[0] for i in os.listdir("assets/example_multi_image")]))
+    images = []
+    for case in multi_case:
+        _images = []
+        for i in range(1, 4):
+            img = Image.open(f'assets/example_multi_image/{case}_{i}.png')
+            W, H = img.size
+            img = img.resize((int(W / H * 512), 512))
+            _images.append(np.array(img))
+        images.append(Image.fromarray(np.concatenate(_images, axis=1)))
+    return images
+
+
+def split_image(image: Image.Image) -> List[Image.Image]:
+    """
+    Split an image into multiple views.
+    """
+    image = np.array(image)
+    alpha = image[..., 3]
+    alpha = np.any(alpha>0, axis=0)
+    start_pos = np.where(~alpha[:-1] & alpha[1:])[0].tolist()
+    end_pos = np.where(alpha[:-1] & ~alpha[1:])[0].tolist()
+    images = []
+    for s, e in zip(start_pos, end_pos):
+        images.append(Image.fromarray(image[:, s:e+1]))
+    return [preprocess_image(image) for image in images]
+
+
 with gr.Blocks(delete_cache=(600, 600)) as demo:
     gr.Markdown("""
     ## Image to 3D Asset with [TRELLIS](https://trellis3d.github.io/)
     * Upload an image and click "Generate" to create a 3D asset. If the image has alpha channel, it be used as the mask. Otherwise, we use `rembg` to remove the background.
     * If you find the generated 3D asset satisfactory, click "Extract GLB" to extract the GLB file and download it.
+    
+    ✨New: 1) Experimental multi-image support. 2) Gaussian file extraction.
     """)
     
     with gr.Row():
         with gr.Column():
-            image_prompt = gr.Image(label="Image Prompt", format="png", image_mode="RGBA", type="pil", height=300)
+            with gr.Tabs() as input_tabs:
+                with gr.Tab(label="Single Image", id=0) as single_image_input_tab:
+                    image_prompt = gr.Image(label="Image Prompt", format="png", image_mode="RGBA", type="pil", height=300)
+                with gr.Tab(label="Multiple Images", id=1) as multiimage_input_tab:
+                    multiimage_prompt = gr.Gallery(label="Image Prompt", format="png", type="pil", height=300, columns=3)
+                    gr.Markdown("""
+                        Input different views of the object in separate images. 
+                        
+                        *NOTE: this is an experimental algorithm without training a specialized model. It may not produce the best results for all images, especially those having different poses or inconsistent details.*
+                    """)
             
             with gr.Accordion(label="Generation Settings", open=False):
                 seed = gr.Slider(0, MAX_SEED, label="Seed", value=0, step=1)
@@ -197,6 +288,7 @@ with gr.Blocks(delete_cache=(600, 600)) as demo:
                 with gr.Row():
                     slat_guidance_strength = gr.Slider(0.0, 10.0, label="Guidance Strength", value=3.0, step=0.1)
                     slat_sampling_steps = gr.Slider(1, 50, label="Sampling Steps", value=12, step=1)
+                multiimage_algo = gr.Radio(["stochastic", "multidiffusion"], label="Multi-image Algorithm", value="stochastic")
 
             generate_btn = gr.Button("Generate")
             
@@ -204,17 +296,26 @@ with gr.Blocks(delete_cache=(600, 600)) as demo:
                 mesh_simplify = gr.Slider(0.9, 0.98, label="Simplify", value=0.95, step=0.01)
                 texture_size = gr.Slider(512, 2048, label="Texture Size", value=1024, step=512)
             
-            extract_glb_btn = gr.Button("Extract GLB", interactive=False)
+            with gr.Row():
+                extract_glb_btn = gr.Button("Extract GLB", interactive=False)
+                extract_gs_btn = gr.Button("Extract Gaussian", interactive=False)
+            gr.Markdown("""
+                        *NOTE: Gaussian file can be very large (~50MB), it will take a while to display and download.*
+                        """)
 
         with gr.Column():
             video_output = gr.Video(label="Generated 3D Asset", autoplay=True, loop=True, height=300)
-            model_output = LitModel3D(label="Extracted GLB", exposure=20.0, height=300)
-            download_glb = gr.DownloadButton(label="Download GLB", interactive=False)
+            model_output = LitModel3D(label="Extracted GLB/Gaussian", exposure=10.0, height=300)
             
+            with gr.Row():
+                download_glb = gr.DownloadButton(label="Download GLB", interactive=False)
+                download_gs = gr.DownloadButton(label="Download Gaussian", interactive=False)  
+    
+    is_multiimage = gr.State(False)
     output_buf = gr.State()
 
     # Example images at the bottom of the page
-    with gr.Row():
+    with gr.Row() as single_image_example:
         examples = gr.Examples(
             examples=[
                 f'assets/example_image/{image}'
@@ -226,16 +327,39 @@ with gr.Blocks(delete_cache=(600, 600)) as demo:
             run_on_click=True,
             examples_per_page=64,
         )
+    with gr.Row(visible=False) as multiimage_example:
+        examples_multi = gr.Examples(
+            examples=prepare_multi_example(),
+            inputs=[image_prompt],
+            fn=split_image,
+            outputs=[multiimage_prompt],
+            run_on_click=True,
+            examples_per_page=8,
+        )
 
     # Handlers
     demo.load(start_session)
     demo.unload(end_session)
     
+    single_image_input_tab.select(
+        lambda: tuple([False, gr.Row.update(visible=True), gr.Row.update(visible=False)]),
+        outputs=[is_multiimage, single_image_example, multiimage_example]
+    )
+    multiimage_input_tab.select(
+        lambda: tuple([True, gr.Row.update(visible=False), gr.Row.update(visible=True)]),
+        outputs=[is_multiimage, single_image_example, multiimage_example]
+    )
+    
     image_prompt.upload(
         preprocess_image,
         inputs=[image_prompt],
         outputs=[image_prompt],
     )
+    multiimage_prompt.upload(
+        preprocess_images,
+        inputs=[multiimage_prompt],
+        outputs=[multiimage_prompt],
+    )
 
     generate_btn.click(
         get_seed,
@@ -243,16 +367,16 @@ with gr.Blocks(delete_cache=(600, 600)) as demo:
         outputs=[seed],
     ).then(
         image_to_3d,
-        inputs=[image_prompt, seed, ss_guidance_strength, ss_sampling_steps, slat_guidance_strength, slat_sampling_steps],
+        inputs=[image_prompt, multiimage_prompt, is_multiimage, seed, ss_guidance_strength, ss_sampling_steps, slat_guidance_strength, slat_sampling_steps, multiimage_algo],
         outputs=[output_buf, video_output],
     ).then(
-        lambda: gr.Button(interactive=True),
-        outputs=[extract_glb_btn],
+        lambda: tuple([gr.Button(interactive=True), gr.Button(interactive=True)]),
+        outputs=[extract_glb_btn, extract_gs_btn],
     )
 
     video_output.clear(
-        lambda: gr.Button(interactive=False),
-        outputs=[extract_glb_btn],
+        lambda: tuple([gr.Button(interactive=False), gr.Button(interactive=False)]),
+        outputs=[extract_glb_btn, extract_gs_btn],
     )
 
     extract_glb_btn.click(
@@ -263,6 +387,15 @@ with gr.Blocks(delete_cache=(600, 600)) as demo:
         lambda: gr.Button(interactive=True),
         outputs=[download_glb],
     )
+    
+    extract_gs_btn.click(
+        extract_gaussian,
+        inputs=[output_buf],
+        outputs=[model_output, download_gs],
+    ).then(
+        lambda: gr.Button(interactive=True),
+        outputs=[download_gs],
+    )
 
     model_output.clear(
         lambda: gr.Button(interactive=False),

trellis/pipelines/trellis_image_to_3d.py

@@ -1,4 +1,5 @@
 from typing import *
+from contextlib import contextmanager
 import torch
 import torch.nn as nn
 import torch.nn.functional as F
@@ -281,3 +282,95 @@ class TrellisImageTo3DPipeline(Pipeline):
         coords = self.sample_sparse_structure(cond, num_samples, sparse_structure_sampler_params)
         slat = self.sample_slat(cond, coords, slat_sampler_params)
         return self.decode_slat(slat, formats)
+
+    @contextmanager
+    def inject_sampler_multi_image(
+        self,
+        sampler_name: str,
+        num_images: int,
+        num_steps: int,
+        mode: Literal['stochastic', 'multidiffusion'] = 'stochastic',
+    ):
+        """
+        Inject a sampler with multiple images as condition.
+        
+        Args:
+            sampler_name (str): The name of the sampler to inject.
+            num_images (int): The number of images to condition on.
+            num_steps (int): The number of steps to run the sampler for.
+        """
+        sampler = getattr(self, sampler_name)
+        setattr(sampler, f'_old_inference_model', sampler._inference_model)
+
+        if mode == 'stochastic':
+            if num_images > num_steps:
+                print(f"\033[93mWarning: number of conditioning images is greater than number of steps for {sampler_name}. "
+                    "This may lead to performance degradation.\033[0m")
+
+            cond_indices = (np.arange(num_steps) % num_images).tolist()
+            def _new_inference_model(self, model, x_t, t, cond, **kwargs):
+                cond_idx = cond_indices.pop(0)
+                cond_i = cond[cond_idx:cond_idx+1]
+                return self._old_inference_model(model, x_t, t, cond=cond_i, **kwargs)
+        
+        elif mode =='multidiffusion':
+            from .samplers import FlowEulerSampler
+            def _new_inference_model(self, model, x_t, t, cond, neg_cond, cfg_strength, cfg_interval, **kwargs):
+                if cfg_interval[0] <= t <= cfg_interval[1]:
+                    preds = []
+                    for i in range(len(cond)):
+                        preds.append(FlowEulerSampler._inference_model(self, model, x_t, t, cond[i:i+1], **kwargs))
+                    pred = sum(preds) / len(preds)
+                    neg_pred = FlowEulerSampler._inference_model(self, model, x_t, t, neg_cond, **kwargs)
+                    return (1 + cfg_strength) * pred - cfg_strength * neg_pred
+                else:
+                    preds = []
+                    for i in range(len(cond)):
+                        preds.append(FlowEulerSampler._inference_model(self, model, x_t, t, cond[i:i+1], **kwargs))
+                    pred = sum(preds) / len(preds)
+                    return pred
+            
+        else:
+            raise ValueError(f"Unsupported mode: {mode}")
+            
+        sampler._inference_model = _new_inference_model.__get__(sampler, type(sampler))
+
+        yield
+
+        sampler._inference_model = sampler._old_inference_model
+        delattr(sampler, f'_old_inference_model')
+
+    @torch.no_grad()
+    def run_multi_image(
+        self,
+        images: List[Image.Image],
+        num_samples: int = 1,
+        seed: int = 42,
+        sparse_structure_sampler_params: dict = {},
+        slat_sampler_params: dict = {},
+        formats: List[str] = ['mesh', 'gaussian', 'radiance_field'],
+        preprocess_image: bool = True,
+        mode: Literal['stochastic', 'multidiffusion'] = 'stochastic',
+    ) -> dict:
+        """
+        Run the pipeline with multiple images as condition
+
+        Args:
+            images (List[Image.Image]): The multi-view images of the assets
+            num_samples (int): The number of samples to generate.
+            sparse_structure_sampler_params (dict): Additional parameters for the sparse structure sampler.
+            slat_sampler_params (dict): Additional parameters for the structured latent sampler.
+            preprocess_image (bool): Whether to preprocess the image.
+        """
+        if preprocess_image:
+            images = [self.preprocess_image(image) for image in images]
+        cond = self.get_cond(images)
+        cond['neg_cond'] = cond['neg_cond'][:1]
+        torch.manual_seed(seed)
+        ss_steps = {**self.sparse_structure_sampler_params, **sparse_structure_sampler_params}.get('steps')
+        with self.inject_sampler_multi_image('sparse_structure_sampler', len(images), ss_steps, mode=mode):
+            coords = self.sample_sparse_structure(cond, num_samples, sparse_structure_sampler_params)
+        slat_steps = {**self.slat_sampler_params, **slat_sampler_params}.get('steps')
+        with self.inject_sampler_multi_image('slat_sampler', len(images), slat_steps, mode=mode):
+            slat = self.sample_slat(cond, coords, slat_sampler_params)
+        return self.decode_slat(slat, formats)

trellis/representations/gaussian/gaussian_model.py

@@ -2,6 +2,7 @@ import torch
 import numpy as np
 from plyfile import PlyData, PlyElement
 from .general_utils import inverse_sigmoid, strip_symmetric, build_scaling_rotation
+import utils3d
 
 
 class Gaussian:
@@ -120,14 +121,21 @@ class Gaussian:
         for i in range(self._rotation.shape[1]):
             l.append('rot_{}'.format(i))
         return l
-
-    def save_ply(self, path):
+        
+    def save_ply(self, path, transform=[[1, 0, 0], [0, 0, -1], [0, 1, 0]]):
         xyz = self.get_xyz.detach().cpu().numpy()
         normals = np.zeros_like(xyz)
         f_dc = self._features_dc.detach().transpose(1, 2).flatten(start_dim=1).contiguous().cpu().numpy()
         opacities = inverse_sigmoid(self.get_opacity).detach().cpu().numpy()
         scale = torch.log(self.get_scaling).detach().cpu().numpy()
         rotation = (self._rotation + self.rots_bias[None, :]).detach().cpu().numpy()
+        
+        if transform is not None:
+            transform = np.array(transform)
+            xyz = np.matmul(xyz, transform.T)
+            rotation = utils3d.numpy.quaternion_to_matrix(rotation)
+            rotation = np.matmul(transform, rotation)
+            rotation = utils3d.numpy.matrix_to_quaternion(rotation)
 
         dtype_full = [(attribute, 'f4') for attribute in self.construct_list_of_attributes()]
 
@@ -137,7 +145,7 @@ class Gaussian:
         el = PlyElement.describe(elements, 'vertex')
         PlyData([el]).write(path)
 
-    def load_ply(self, path):
+    def load_ply(self, path, transform=[[1, 0, 0], [0, 0, -1], [0, 1, 0]]):
         plydata = PlyData.read(path)
 
         xyz = np.stack((np.asarray(plydata.elements[0]["x"]),
@@ -172,6 +180,13 @@ class Gaussian:
         for idx, attr_name in enumerate(rot_names):
             rots[:, idx] = np.asarray(plydata.elements[0][attr_name])
             
+        if transform is not None:
+            transform = np.array(transform)
+            xyz = np.matmul(xyz, transform)
+            rotation = utils3d.numpy.quaternion_to_matrix(rotation)
+            rotation = np.matmul(rotation, transform)
+            rotation = utils3d.numpy.matrix_to_quaternion(rotation)
+            
         # convert to actual gaussian attributes
         xyz = torch.tensor(xyz, dtype=torch.float, device=self.device)
         features_dc = torch.tensor(features_dc, dtype=torch.float, device=self.device).transpose(1, 2).contiguous()

trellis/utils/postprocessing_utils.py

@@ -14,6 +14,7 @@ import cv2
 from PIL import Image
 from .random_utils import sphere_hammersley_sequence
 from .render_utils import render_multiview
+from ..renderers import GaussianRenderer
 from ..representations import Strivec, Gaussian, MeshExtractResult
 
 
@@ -454,5 +455,133 @@ def to_glb(
 
     # rotate mesh (from z-up to y-up)
     vertices = vertices @ np.array([[1, 0, 0], [0, 0, -1], [0, 1, 0]])
-    mesh = trimesh.Trimesh(vertices, faces, visual=trimesh.visual.TextureVisuals(uv=uvs, image=texture))
+    material = trimesh.visual.material.PBRMaterial(
+        roughnessFactor=1.0,
+        baseColorTexture=texture,
+        baseColorFactor=np.array([255, 255, 255, 255], dtype=np.uint8)
+    )
+    mesh = trimesh.Trimesh(vertices, faces, visual=trimesh.visual.TextureVisuals(uv=uvs, material=material))
     return mesh
+
+
+def simplify_gs(
+    gs: Gaussian,
+    simplify: float = 0.95,
+    verbose: bool = True,
+):
+    """
+    Simplify 3D Gaussians
+    NOTE: this function is not used in the current implementation for the unsatisfactory performance.
+    
+    Args:
+        gs (Gaussian): 3D Gaussian.
+        simplify (float): Ratio of Gaussians to remove in simplification.
+    """
+    if simplify <= 0:
+        return gs
+    
+    # simplify
+    observations, extrinsics, intrinsics = render_multiview(gs, resolution=1024, nviews=100)
+    observations = [torch.tensor(obs / 255.0).float().cuda().permute(2, 0, 1) for obs in observations]
+    
+    # Following https://arxiv.org/pdf/2411.06019
+    renderer = GaussianRenderer({
+            "resolution": 1024,
+            "near": 0.8,
+            "far": 1.6,
+            "ssaa": 1,
+            "bg_color": (0,0,0),
+        })
+    new_gs = Gaussian(**gs.init_params)
+    new_gs._features_dc = gs._features_dc.clone()
+    new_gs._features_rest = gs._features_rest.clone() if gs._features_rest is not None else None
+    new_gs._opacity = torch.nn.Parameter(gs._opacity.clone())
+    new_gs._rotation = torch.nn.Parameter(gs._rotation.clone())
+    new_gs._scaling = torch.nn.Parameter(gs._scaling.clone())
+    new_gs._xyz = torch.nn.Parameter(gs._xyz.clone())
+    
+    start_lr = [1e-4, 1e-3, 5e-3, 0.025]
+    end_lr = [1e-6, 1e-5, 5e-5, 0.00025]
+    optimizer = torch.optim.Adam([
+        {"params": new_gs._xyz, "lr": start_lr[0]},
+        {"params": new_gs._rotation, "lr": start_lr[1]},
+        {"params": new_gs._scaling, "lr": start_lr[2]},
+        {"params": new_gs._opacity, "lr": start_lr[3]},
+    ], lr=start_lr[0])
+    
+    def exp_anealing(optimizer, step, total_steps, start_lr, end_lr):
+            return start_lr * (end_lr / start_lr) ** (step / total_steps)
+
+    def cosine_anealing(optimizer, step, total_steps, start_lr, end_lr):
+        return end_lr + 0.5 * (start_lr - end_lr) * (1 + np.cos(np.pi * step / total_steps))
+    
+    _zeta = new_gs.get_opacity.clone().detach().squeeze()
+    _lambda = torch.zeros_like(_zeta)
+    _delta = 1e-7
+    _interval = 10
+    num_target = int((1 - simplify) * _zeta.shape[0])
+    
+    with tqdm(total=2500, disable=not verbose, desc='Simplifying Gaussian') as pbar:
+        for i in range(2500):
+            # prune
+            if i % 100 == 0:
+                mask = new_gs.get_opacity.squeeze() > 0.05
+                mask = torch.nonzero(mask).squeeze()
+                new_gs._xyz = torch.nn.Parameter(new_gs._xyz[mask])
+                new_gs._rotation = torch.nn.Parameter(new_gs._rotation[mask])
+                new_gs._scaling = torch.nn.Parameter(new_gs._scaling[mask])
+                new_gs._opacity = torch.nn.Parameter(new_gs._opacity[mask])
+                new_gs._features_dc = new_gs._features_dc[mask]
+                new_gs._features_rest = new_gs._features_rest[mask] if new_gs._features_rest is not None else None
+                _zeta = _zeta[mask]
+                _lambda = _lambda[mask]
+                # update optimizer state
+                for param_group, new_param in zip(optimizer.param_groups, [new_gs._xyz, new_gs._rotation, new_gs._scaling, new_gs._opacity]):
+                    stored_state = optimizer.state[param_group['params'][0]]
+                    if 'exp_avg' in stored_state:
+                        stored_state['exp_avg'] = stored_state['exp_avg'][mask]
+                        stored_state['exp_avg_sq'] = stored_state['exp_avg_sq'][mask]
+                    del optimizer.state[param_group['params'][0]]
+                    param_group['params'][0] = new_param
+                    optimizer.state[param_group['params'][0]] = stored_state
+
+            opacity = new_gs.get_opacity.squeeze()
+            
+            # sparisfy
+            if i % _interval == 0:
+                _zeta = _lambda + opacity.detach()
+                if opacity.shape[0] > num_target:
+                    index = _zeta.topk(num_target)[1]
+                    _m = torch.ones_like(_zeta, dtype=torch.bool)
+                    _m[index] = 0
+                    _zeta[_m] = 0
+                _lambda = _lambda + opacity.detach() - _zeta
+            
+            # sample a random view
+            view_idx = np.random.randint(len(observations))
+            observation = observations[view_idx]
+            extrinsic = extrinsics[view_idx]
+            intrinsic = intrinsics[view_idx]
+            
+            color = renderer.render(new_gs, extrinsic, intrinsic)['color']
+            rgb_loss = torch.nn.functional.l1_loss(color, observation)
+            loss = rgb_loss + \
+                   _delta * torch.sum(torch.pow(_lambda + opacity - _zeta, 2))
+            
+            optimizer.zero_grad()
+            loss.backward()
+            optimizer.step()
+            
+            # update lr
+            for j in range(len(optimizer.param_groups)):
+                optimizer.param_groups[j]['lr'] = cosine_anealing(optimizer, i, 2500, start_lr[j], end_lr[j])
+            
+            pbar.set_postfix({'loss': rgb_loss.item(), 'num': opacity.shape[0], 'lambda': _lambda.mean().item()})
+            pbar.update()
+            
+    new_gs._xyz = new_gs._xyz.data
+    new_gs._rotation = new_gs._rotation.data
+    new_gs._scaling = new_gs._scaling.data
+    new_gs._opacity = new_gs._opacity.data
+    
+    return new_gs